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1.
研究了环扩张下的Gorenstein平坦模型结构及其同伦范畴,设R≤S是满足一些条件的平坦扩张.我们证明了若f:M→N在S-模范畴的Gorenstein平坦模型结构中是上纤维化(纤维化,弱等价),则f:M→N在R-模范畴中亦如此;若R≤S是优越扩张,反过来也成立,即在优越扩张下Gorenstein平坦模型结构是不变的.进而,相关的稳定范畴是等价的,当且仅当对任意Gorenstein平坦S-模M,Coker(ηM)是平坦的,其中η表示S-模范畴和R-模范畴间的Quillen伴随函子的单位. 相似文献
2.
George Voutsadakis 《Mathematical Logic Quarterly》2003,49(4):347-352
Equivalent deductive systems were introduced in [4] with the goal of treating 1‐deductive systems and algebraic 2‐deductive systems in a uniform way. Results of [3], appropriately translated and strengthened, show that two deductive systems over the same language type are equivalent if and only if their lattices of theories are isomorphic via an isomorphism that commutes with substitutions. Deductive equivalence of π‐institutions [14, 15] generalizes the notion of equivalence of deductive systems. In [15, Theorem 10.26] this criterion for the equivalence of deductive systems was generalized to a criterion for the deductive equivalence of term π‐institutions, forming a subclass of all π‐institutions that contains those π‐institutions directly corresponding to deductive systems. This criterion is generalized here to cover the case of arbitrary π‐institutions. 相似文献
3.
Ulrich Knauer 《Semigroup Forum》1971,3(1):359-370
In this paper we shall consider a non-additive category of A-modules, that is, instead of a ring A we take a monoid A which
acts on sets from the left. These objects will be called A-acts. We investigate indecomposable A-acts and generators and characterize
projectives in this category. For a given monoid A we describe all monoids B such that the category of B-acts is equivalent
to the category of A-acts. In particular we find that equivalence of these categories yields an isomorphism between the monoids
A and B if A is a group or finite or commutative. This differs from the additive case where the categories of modules over
a commutative field and its ring of nxn matrices are equivalent. Finally we give examples of non-isomorphic monoids A and
B such that the corresponding categories are equivalent. 相似文献
4.
K. J. Horadam 《Journal of Algebraic Combinatorics》2012,35(3):477-496
Two types of equivalence relation are used to classify functions between finite groups into classes which preserve combinatorial
and algebraic properties important for a wide range of applications. However, it is very difficult to tell when functions
equivalent under the coarser (“graph”) equivalence are inequivalent under the finer (“bundle”) equivalence. Here we relate
graphs to transversals and splitting relative difference sets (RDSs) and introduce an intermediate relation, canonical equivalence,
to aid in distinguishing the classes. We identify very precisely the conditions under which a graph equivalence determines
a bundle equivalence, using transversals and extensions. We derive a new and easily computed algebraic measure of nonlinearity
for a function f, calculated from the image of its coboundary ∂f. This measure is preserved by bundle equivalence but not by the coarser equivalences. It takes its minimum value if f is a homomorphism, and takes its maximum value if the graph of f contains a splitting RDS. 相似文献
5.
6.
Yves Diers 《Journal of Geometry》1999,65(1-2):54-76
For an arbitrary algebraic theory T and a prescribed T-algebraL, the geometrical category AfAlgSet(L) of affine algebraic sets over the affine lineL is build up. It is proved to be dually equivalent to the category FcAlg(L) of functional T-algebras overL. The Galois theory ofL is defined and a Galois duality established. These geometrical categories are characterized up to an equivalence of categories. 相似文献
7.
Toke Meier Carlsen Søren Eilers Eduard Ortega Gunnar Restorff 《Journal of Mathematical Analysis and Applications》2019,469(2):1088-1110
We give conditions for when continuous orbit equivalence of one-sided shift spaces implies flow equivalence of the associated two-sided shift spaces. Using groupoid techniques, we prove that this is always the case for shifts of finite type. This generalises a result of Matsumoto and Matui from the irreducible to the general case. We also prove that a pair of one-sided shift spaces of finite type are continuously orbit equivalent if and only if their groupoids are isomorphic, and that the corresponding two-sided shifts are flow equivalent if and only if the groupoids are stably isomorphic. As applications we show that two finite directed graphs with no sinks and no sources are move equivalent if and only if the corresponding graph -algebras are stably isomorphic by a diagonal-preserving isomorphism (if and only if the corresponding Leavitt path algebras are stably isomorphic by a diagonal-preserving isomorphism), and that two topological Markov chains are flow equivalent if and only if there is a diagonal-preserving isomorphism between the stabilisations of the corresponding Cuntz–Krieger algebras (the latter generalises a result of Matsumoto and Matui about irreducible topological Markov chains with no isolated points to a result about general topological Markov chains). We also show that for general shift spaces, strongly continuous orbit equivalence implies two-sided conjugacy. 相似文献
8.
Valdis Laan 《Periodica Mathematica Hungarica》2010,60(1):81-94
Two semigroups are called strongly Morita equivalent if they are contained in a Morita context with unitary bi-acts and surjective
mappings. We consider the notion of context equivalence which is obtained from the notion of strong Morita equivalence by
dropping the requirement of unitariness. We show that context equivalence is an equivalence relation on the class of factorisable
semigroups and describe factorisable semigroups that are context equivalent to monoids or groups, and semigroups with weak
local units that are context equivalent to inverse semigroups, orthodox semigroups or semilattices. 相似文献
9.
Motivated by the problem of Hurwitz equivalence of Δ2 factorization in the braid group, we address the problem of Hurwitz equivalence in the symmetric group, of 1s
n
factorizations with transposition factors. Looking at the transpositions as the edges in a graph, we show that two factorizations
are Hurwitz equivalent if and only if their graphs have the same weighted connected components. The graph structure allows
us to compute Hurwitz equivalence in the symmetric group. Using this result, one can compute non-Hurwitz equivalence in the
braid group.
This paper is part of the author’s PhD thesis.
This work was partially supported by the Emmy Noether Research Institute for Mathematics (center of the Minerva Foundation
of Germany), the Excellency Center “Group Theoretic Methods in the Study of Algebraic Varieties” of the Israel Science Foundation,
and by EAGER (EU network, HPRN-CT-2009-00099). Received December 31, 2001 and in revised form August 6, 2002 相似文献
10.
《International Journal of Approximate Reasoning》2009,50(3):678-688
The notion of regular equivalence or bisimulation arises in different applications, such as positional analysis of social networks and behavior analysis of state transition systems. The common characteristic of these applications is that the system under modeling can be represented as a graph. Thus, regular equivalence is a notion used to capture the similarity between nodes based on their linking patterns with other nodes. According to Borgatti and Everett, two nodes are regularly equivalent if they are equally related to equivalent others. In recent years, fuzzy graphs have also received considerable attention because they can represent both the qualitative relationships and the degrees of connection between nodes. In this paper, we generalize the notion of regular equivalence to fuzzy graphs based on two alternative definitions of regular equivalence. While the two definitions are equivalent for crisp graphs, they induce different generalizations for fuzzy graphs. The first generalization, called regular similarity, is based on the characterization of regular equivalence as an equivalence relation that commutes with the underlying graph edges. The regular similarity is then a fuzzy binary relation that specifies the degree of similarity between nodes in the graph. The second generalization, called generalized regular equivalence, is based on the definition of coloring. A coloring is a mapping from the set of nodes to a set of colors. A coloring is regular if nodes that are mapped to the same color, have the same colors in their neighborhoods. Hence, generalized regular equivalence is an equivalence relation that can determine a crisp partition of the nodes in a fuzzy graph. 相似文献
11.
Suppose k is a field. Let A and B be two finite dimensional k-algebras such that there is a stable equivalence of Morita type between A and B. In this paper, we prove that (1) if A and B are representation-finite then their Auslander algebras are stably equivalent of Morita type; (2) The n-th Hochschild homology groups of A and B are isomorphic for all n≥1. A new proof is also provided for Hochschild cohomology groups of self-injective algebras under a stable equivalence of Morita type. 相似文献
12.
We define relative Goursat categories and prove relative versions of the equivalent conditions defining regular Goursat categories. These include 3-permutability of equivalence relations, preservation of equivalence relations under direct images, a condition on so-called Goursat pushouts, and the denormalised 3×3 Lemma. This extends recent work by Gran and Rodelo on a new characterisation of Goursat categories to a relative context. 相似文献
13.
Vyacheslav Kulagin 《Israel Journal of Mathematics》2006,152(1):83-104
We study cocycles of an ergodic generic countable equivalence relation ℜ modulo meager sets. Two cocycles of ℜ are called
weakly equivalent if they are cohomologous up to an element of Aut ℜ. It is proved that two nontransient cocycles with values
in an arbitrary countable group are weakly equivalent if and only if their generic Mackey actions are isomorphic. 相似文献
14.
We extend the notion of stable equivalence to the class of locally finite graded algebras. For such an algebra Λ, we focus on the Krull–Schmidt category grΛ of finitely generated -graded Λ-modules with degree 0 maps, and the stable category obtained by factoring out those maps that factor through a graded projective module. We say that Λ and Γ are graded stably equivalent if there is an equivalence that commutes with the grading shift. Adapting arguments of Auslander and Reiten involving functor categories, we show that a graded stable equivalence α commutes with the syzygy operator (where defined) and preserves finitely presented modules. As a result, we see that if Λ is right noetherian (resp. right graded coherent), then so is any graded stably equivalent algebra. Furthermore, if Λ is right noetherian or k is artinian, we use almost split sequences to show that a graded stable equivalence preserves finite length modules. Of particular interest in the nonartinian case, we prove that any graded stable equivalence involving an algebra Λ with socΛ=0 must be a graded Morita equivalence. 相似文献
15.
We prove that a coherent DQ-kernel induces an equivalence between the derived categories of DQ-modules with coherent cohomology if and only if the graded commutative kernel associated to it induces an equivalence between the derived categories of coherent sheaves. 相似文献
16.
In this paper we study the notion of knowledge from the positions of universal algebra and algebraic logic. We consider first
order knowledge which is based on first order logic. We define categories of knowledge and knowledge base models. These notions
are defined for the fixed subject of knowledge. The key notion of informational equivalence of two knowledge base models is
introduced. We use the idea of equivalence of categories in this definition. We prove that for finite models there is a clear
way to determine whether the knowledge base models are informationally equivalent. 相似文献
17.
We establish a correspondence between recollements of abelian categories up to equivalence and certain TTF-triples. For a module category we show, moreover, a correspondence with idempotent ideals, recovering a theorem of Jans. Furthermore, we show that a recollement whose terms are module categories is equivalent to one induced by an idempotent element, thus answering a question by Kuhn. 相似文献
18.
Michihisa Wakui 《Algebras and Representation Theory》2004,7(5):491-515
We determine various additional structures on all nonsemisimple Hopf algebras of dimension 8 over an algebraically closed
field k of characteristic 0, including their representation rings and quasitriangular structures. As a consequence, it is shown that
for two such Hopf algebras, the tensor categories of their representations are monoidally equivalent if and only if the representation
rings of them are isomorphic as rings.
An erratum to this article is available at . 相似文献
19.
A finite, nontrivial algebra is order-primal if its term functions are precisely the monotone functions for some order on the underlying set. We show that the prevariety generated by an order-primal algebra P is relatively congruence-distributive and that the variety generated by P is congruence-distributive if and only if it contains at most two non-ismorphic subdirectly irreducible algebras. We also prove that if the prevarieties generated by order-primal algebras P and Q are equivalent as categories, then the corresponding orders or their duals generate the same order variety. A large class of order-primal algebras is described each member of which generates a variety equivalent as a category to the variety determined by the six-element, bounded ordered set which is not a lattice. These results are proved by considering topological dualities with particular emphasis on the case where there is a monotone near-unanimity function.This research was carried out while the third author held a research fellowship at La Trobe University supported by ARGS grant B85154851. The second author was supported by a grant from the NSERC. 相似文献
20.
A Steiner triple system of order v, STS(v), may be called equivalent to another STS(v) if one can be converted to the other by a sequence of three simple operations involving Pasch trades with a single negative block. It is conjectured that any two STS(v)s on the same base set are equivalent in this sense. We prove that the equivalence class containing a given system S on a base set V contains all the systems that can be obtained from S by any sequence of well over one hundred distinct trades, and that this equivalence class contains all isomorphic copies of S on V. We also show that there are trades which cannot be effected by means of Pasch trades with a single negative block. 相似文献