共查询到20条相似文献,搜索用时 46 毫秒
1.
Alexander J. Diesl Thomas J. Dorsey Shelly Garg Dinesh Khurana 《Journal of Pure and Applied Algebra》2014
Many authors have investigated the behavior of strong cleanness under certain ring extensions. In this note, we investigate the classical problem of lifting idempotents, in order to consolidate and extend these results. Our main result is that if R is a ring which is complete with respect to an ideal I and if x is an element of R whose image in R/I is strongly π-regular, then x is strongly clean in R. This generalizes Theorem 2.1 of Chen and Zhou (2007) [9]. 相似文献
2.
3.
The sensitivity set of a Boolean function at a particular input is the set of input positions where changing that one bit changes the output. Analogously we define the sensitivity set of a Boolean formula in a conjunctive normal form at a particular truth assignment, it is the set of positions where changing that one bit of the truth assignment changes the evaluation of at least one of the conjunct in the formula. We consider Boolean formulas in a generalized conjunctive normal form. Given a set ? of Boolean functions, an ?-constraint is an application of a function from ? to a tuple of literals built upon distinct variables, an ?-formula is then a conjunction of ?-constraints. In this framework, given a truth assignment I and a set of positions S, we are able to enumerate all ?-formulas that are satisfied by I and that have S as the sensitivity set at I. We prove that this number depends on the cardinality of S only, and can be expressed according to the sensitivity of the Boolean functions in ?. 相似文献
4.
Let G be a group. Any G-module M has an algebraic structure called a G-family of Alexander quandles. Given a 2-cocycle of a cohomology associated with this G-family, topological invariants of (handlebody) knots in the 3-sphere are defined. We develop a simple algorithm to algebraically construct n-cocycles of this G-family from G-invariant group n-cocycles of the abelian group M. We present many examples of 2-cocycles of these G-families using facts from (modular) invariant theory. 相似文献
5.
Mathias Beiglböck Walter SchachermayerBezirgen Veliyev 《Stochastic Processes and their Applications》2012
Every submartingale S of class D has a unique Doob–Meyer decomposition S=M+A, where M is a martingale and A is a predictable increasing process starting at 0. 相似文献
6.
A context-free grammar G over an alphabet A is defined as a set of substitution rules that replace a letter in A by a formal function over A. The purpose of this paper is to show that some combinatorial arrays, such as the Catalan’s triangle, can be generated by context-free grammars in three variables. 相似文献
8.
Let G=(V,E) be a graph. A subset D⊆V is a dominating set if every vertex not in D is adjacent to a vertex in D. A dominating set D is called a total dominating set if every vertex in D is adjacent to a vertex in D. The domination (resp. total domination) number of G is the smallest cardinality of a dominating (resp. total dominating) set of G. The bondage (resp. total bondage) number of a nonempty graph G is the smallest number of edges whose removal from G results in a graph with larger domination (resp. total domination) number of G. The reinforcement (resp. total reinforcement) number of G is the smallest number of edges whose addition to G results in a graph with smaller domination (resp. total domination) number. This paper shows that the decision problems for the bondage, total bondage, reinforcement and total reinforcement numbers are all NP-hard. 相似文献
9.
10.
Let S be a positively graded polynomial ring over a field of characteristic 0, and I⊂S a proper graded ideal. In this note it is shown that S/I is Golod if ∂(I)2⊂I. Here ∂(I) denotes the ideal generated by all the partial derivatives of elements of I. We apply this result to find large classes of Golod ideals, including powers, symbolic powers, and saturations of ideals. 相似文献
11.
We develop a notion of nonlinear expectation–G-expectation–generated by a nonlinear heat equation with infinitesimal generator G. We first study multi-dimensional G-normal distributions. With this nonlinear distribution we can introduce our G-expectation under which the canonical process is a multi-dimensional G-Brownian motion. We then establish the related stochastic calculus, especially stochastic integrals of Itô’s type with respect to our G-Brownian motion, and derive the related Itô’s formula. We have also obtained the existence and uniqueness of stochastic differential equations under our G-expectation. 相似文献
12.
Mustapha Chellali Teresa W. Haynes Stephen T. Hedetniemi Alice McRae 《Discrete Applied Mathematics》2013
A subset S⊆V in a graph G=(V,E) is a [j,k]-set if, for every vertex v∈V?S, j≤|N(v)∩S|≤k for non-negative integers j and k, that is, every vertex v∈V?S is adjacent to at least j but not more than k vertices in S. In this paper, we focus on small j and k, and relate the concept of [j,k]-sets to a host of other concepts in domination theory, including perfect domination, efficient domination, nearly perfect sets, 2-packings, and k-dependent sets. We also determine bounds on the cardinality of minimum [1, 2]-sets, and investigate extremal graphs achieving these bounds. This study has implications for restrained domination as well. Using a result for [1, 3]-sets, we show that, for any grid graph G, the restrained domination number is equal to the domination number of G. 相似文献
13.
We show that, for any compact Alexandrov surface S (without boundary) and any point y in S, there exists a point x in S for which y is a critical point. Moreover, we prove that uniqueness characterizes the surfaces homeomorphic to the sphere among smooth orientable surfaces. 相似文献
14.
By means of a certain module V and its tensor powers in a finite tensor category, we study a question of whether the depth of a Hopf subalgebra R of a finite-dimensional Hopf algebra H is finite. The module V is the counit representation induced from R to H, which is then a generalized permutation module, as well as a module coalgebra. We show that if in the subalgebra pair either Hopf algebra has finite representation type, or V is either semisimple with R∗ pointed, projective, or its tensor powers satisfy a Burnside ring formula over a finite set of Hopf subalgebras including R, then the depth of R in H is finite. One assigns a nonnegative integer depth to V, or any other H-module, by comparing the truncated tensor algebras of V in a finite tensor category and so obtains upper and lower bounds for depth of a Hopf subalgebra. For example, a relative Hopf restricted module has depth 1, and a permutation module of a corefree subgroup has depth less than the number of values of its character. 相似文献
15.
We prove the Arad–Herzog conjecture for various families of finite simple groups — if A and B are nontrivial conjugacy classes, then AB is not a conjugacy class. We also prove that if G is a finite simple group of Lie type and A and B are nontrivial conjugacy classes, either both semisimple or both unipotent, then AB is not a conjugacy class. We also prove a strong version of the Arad–Herzog conjecture for simple algebraic groups and in particular show that almost always the product of two conjugacy classes in a simple algebraic group consists of infinitely many conjugacy classes. As a consequence we obtain a complete classification of pairs of centralizers in a simple algebraic group which have dense product. A special case of this has been used by Prasad to prove a uniqueness result for Tits systems in quasi-reductive groups. Our final result is a generalization of the Baer–Suzuki theorem for p-elements with p≥5. 相似文献
16.
Let X be a (real) Banach space, A be a subset of X and x∉A. We present cone-separation in terms of separation by a collection of linear functionals defined on X and obtain necessary and sufficient conditions for cone-separability A and x. Also, we give characterizations for star-shaped separability. Finally, as an application of separability, we characterize best approximation problem by elements of star-shaped sets. 相似文献
17.
A tournament of order n is usually considered as an orientation of the complete graph Kn. In this note, we consider a more general definition of a tournament that we call aC-tournament, where C is the adjacency matrix of a multigraph G, and a C-tournament is an orientation of G. The score vector of a C-tournament is the vector of outdegrees of its vertices. In 1965 Hakimi obtained necessary and sufficient conditions for the existence of a C-tournament with a prescribed score vector R and gave an algorithm to construct such a C-tournament which required, however, some backtracking. We give a simpler and more transparent proof of Hakimi’s theorem, and then provide a direct construction of such a C-tournament which works even for weighted graphs. 相似文献
18.
A polychromatic k-coloring of a map G on a surface is a k-coloring such that each face of G has all k colors on its boundary vertices. An even embedding G on a surface is a map of a simple graph on the surface such that each face of G is bounded by a cycle of even length. In this paper, we shall prove that a cubic even embedding G on the projective plane has a polychromatic proper 4-coloring if and only if G is not isomorphic to a Möbius ladder with an odd number of rungs. For proving the theorem, we establish a generating theorem for 3-connected Eulerian multi-triangulations on the projective plane. 相似文献
19.
Let R(G) be the graph obtained from G by adding a new vertex corresponding to each edge of G and by joining each new vertex to the end vertices of the corresponding edge, and Q(G) be the graph obtained from G by inserting a new vertex into every edge of G and by joining by edges those pairs of these new vertices which lie on adjacent edges of G. In this paper, we determine the Laplacian polynomials of R(G) and Q(G) of a regular graph G; on the other hand, we derive formulae and lower bounds of the Kirchhoff index of these graphs. 相似文献
20.
We analyze the extent to which a quantum universal enveloping algebra of a Kac–Moody algebra g is defined by multidegrees of its defining relations. To this end, we consider a class of character Hopf algebras defined by the same number of defining relations of the same degrees as the Kac–Moody algebra g. We demonstrate that if the generalized Cartan matrix A of g is connected then the algebraic structure, up to a finite number of exceptional cases, is defined by just one “continuous” parameter q related to a symmetrization of A, and one “discrete” parameter m related to the modular symmetrizations of A. The Hopf algebra structure is defined by n(n−1)/2 additional “continuous” parameters. We also consider the exceptional cases for Cartan matrices of finite or affine types in more detail, establishing the number of exceptional parameter values in terms of the Fibonacci sequence. 相似文献