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1.
Loday and Ronco introduced the notion of a trioid and constructed the free trioid of rank 1. This paper is devoted to the study of congruences on trioids. We characterize the least dimonoid congruences and the least semigroup congruence on the free (commutative, rectangular) trioid. 相似文献
2.
A. V. Zhuchok 《Algebra and Logic》2011,50(4):323-340
It is proved that a system of axioms for a dimonoid is independent and Cayley’s theorem for semigroups has an analog in the
class of dimonoids. The least separative congruence is constructed on an arbitrary dimonoid endowed with a commutative operation.
It is shown that an appropriate quotient dimonoid is a commutative separative semigroup. The least separative congruence on
a free commutative dimonoid is characterized. It is stated that each dimonoid with a commutative operation is a semilattice
of Archimedean subdimonoids, each dimonoid with a commutative periodic semigroup is a semilattice of unipotent subdimonoids,
and each dimonoid with a commutative operation is a semilattice of a-connected subdimonoids. Various dimonoid constructions are presented. 相似文献
3.
Karl Auinger 《Monatshefte für Mathematik》1987,104(1):1-15
A construction of all globally idempotent semigroups with Boolean (complemented modular, relatively complemented, sectionally complemented, respectively) congruence lattice is given. Furthermore, it is shown that an arbitrary semigroup has Boolean (...) congruence lattice if and only if it is a special kind of inflation of a semigroup of the foregoing type. As applications, all commutative, finite, and completely semisimple semigroups, respectively, with Boolean (...) congruence lattice are completely determined. 相似文献
5.
Anatolii V. Zhuchok 《代数通讯》2018,46(8):3262-3279
We consider strong doppelsemigroups which are sets with two binary associative operations satisfying axioms of strong interassociativity. Commutative dimonoids in the sense of Loday are examples of strong doppelsemigroups and two strongly interassociative semigroups give rise to a strong doppelsemigroup. The main aim of this paper is to construct a free strong doppelsemigroup, a free n-dinilpotent strong doppelsemigroup, a free commutative strong doppelsemigroup and a free n-nilpotent strong doppelsemigroup. We also characterize the least n-dinilpotent congruence, the least commutative congruence, the least n-nilpotent congruence on a free strong doppelsemigroup and establish that the automorphism group of every constructed free algebra is isomorphic to the symmetric group. 相似文献
6.
交换分配半环上的最小分配格同余 总被引:4,自引:0,他引:4
§ 1 . Introduction AsemiringSisanalgebraicstructure(S ,+,·)consistingofanon emptysetStogetherwithtwobinaryoperations +and·onSsuchthat(S ,+)and(S ,·)aresemigroupsconnectedbyring likedistributivity[1 ] .AsemiringSiscalledacommutativesemiringif (S ,+)and(S ,·)arebothcommutative.AcommutativesemiringiscalledacommutativedistributivityifinStheadditionisdistributiveaboutmultiplication ,i.e.,ab +c =(a+c) (b+c) ,a +bc=(a +b) (a+c) holdsforalla ,b,c∈S[2 ] .Anequivalentrelationρonasemiring… 相似文献
7.
Anatolii V. Zhuchok 《Algebra Universalis》2017,77(3):361-374
In this paper, we consider doppelsemigroups, which are sets with two binary associative operations satisfying additional axioms. Commutative dimonoids in the sense of Loday are examples of doppelsemigroups and two interassociative semigroups give rise to a doppelsemigroup. The main result of this paper is the construction of the free product of doppelsemigroups. We also construct the free doppelsemigroup, the free commutative doppelsemigroup, the free n-nilpotent doppelsemigroup, and characterize the least commutative congruence and the least n-nilpotent congruence on a free doppelsemigroup. 相似文献
8.
9.
乔占科 《纯粹数学与应用数学》1995,(1)
本文分别给出П正则半群的幂等元同余类和Пorthodox半群[1]的幂等元同余类的П正则性刻画.其次,证明П逆半群或完全П正则半群S的幂等元同余类是S的П正则子半群.最后讨论orthodox半群的幂等元同合类的正则性. 相似文献
10.
Jakub Opršal 《Order》2018,35(3):433-460
We provide a partial result on Taylor’s modularity conjecture, and several related problems. Namely, we show that the interpretability join of two idempotent varieties that are not congruence modular is not congruence modular either, and we prove an analog for idempotent varieties with a cube term. Also, similar results are proved for linear varieties and the properties of congruence modularity, having a cube term, congruence n-permutability for a fixed n, and satisfying a non-trivial congruence identity. 相似文献
11.
A submodule N of a module M is idempotent if N = Hom(M, N)N. The module M is fully idempotent if every submodule of M is idempotent. We prove that over a commutative ring, cyclic idempotent submodules of any module are direct summands. Counterexamples are given to show that this result is not true in general. It is shown that over commutative Noetherian rings, the fully idempotent modules are precisely the semisimple modules. We also show that the commutative rings over which every module is fully idempotent are exactly the semisimple rings. Idempotent submodules of free modules are characterized. 相似文献
12.
Brent Kerby 《Journal of Combinatorial Theory, Series A》2011,118(8):2232-2245
Norton and Stein associated a number with each idempotent quasigroup or diagonalized Latin square of given finite order n, showing that it is congruent mod 2 to the triangular number T(n). In this paper, we use a graph-theoretic approach to extend their invariant to an arbitrary finite quasigroup. We call it the cycle number, and identify it as the number of connected components in a certain graph, the cycle graph. The congruence obtained by Norton and Stein extends to the general case, giving a simplified proof (with topology replacing case analysis) of the well-known congruence restriction on the possible orders of general Schroeder quasigroups. Cycle numbers correlate nicely with algebraic properties of quasigroups. Certain well-known classes of quasigroups, such as Schroeder quasigroups and commutative Moufang loops, are shown to maximize the cycle number among all quasigroups belonging to a more general class. 相似文献
13.
Amir Ehsani 《Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences)》2011,46(1):56-60
In this paper a generalized entropic property is defined for a pair of operations. We show that for an idempotent algebra A = (A, f, g) with two ternary operations, if one of f or g is commutative and the pair of operations (f, g) satisfies the generalized entropic property, then (f, g) is entropic. Also, it is proved that every idempotent, commutative algebra A = (A, f, g) with a ternary and a binary operation, satisfying the generalized entropic property, is entropic. 相似文献
14.
给出模糊集Quantale的定义,在此基础上对Quantale与它对应的模糊集Quantale二者之间的关系进行比较,得到如果一个Quantale是可换的、单位的,则它的模糊集Quantale也是可换的、单位的结论。然后给出Quantale的一种嵌入方式。 相似文献
15.
Mario Petrich 《Semigroup Forum》2005,71(3):366-388
On any regular semigroup S, the greatest idempotent pure congruence
τ the greatest idempotent separating congruence μ and the least
band congruence β are used to give the S-classification of regular semigroups as follows. These congruences generate a sublattice
Λ of the congruence lattice C(S) of S. We consider the triples (Λ,K,T), where K and T are the restrictions of the K- and T-relations
on C(S) to Λ. Such triples are characterized abstractly and form the objects of a category S whose morphisms are surjective K- and T-preserving homomorphisms subject to a mild condition. The class of regular semigroups
is made into a category S whose morphisms are fairly restricted homomorphisms. The main result of the paper is the existence of a representative functor
from S to S. The effect of the S-classification on Reilly semigroups and cryptogroups is discussed briefly. 相似文献
16.
In a natural way we can “lift” any operation defined on a set A to an operation on the set of all non-empty subsets of A and obtain from any algebra (A, Ω) its power algebra of subsets. In this paper we investigate extended power algebras (power algebras of non-empty subsets with one additional
semilattice operation) of modes (entropic and idempotent algebras). We describe some congruence relations on these algebras
such that their quotients are idempotent. Such congruences determine some class of non-trivial subvarieties of the variety
of all semilattice ordered modes (modals). 相似文献
17.
Varieties of idempotent semirings with commutative addition 总被引:3,自引:0,他引:3
The multiplicative reduct of an idempotent semiring with commutative addition is a regular band. Accordingly there are 13
distinct varieties consisting of idempotent semirings with commutative addition corresponding to the 13 subvarieties of the
variety of regular bands. The lattice generated by the these 13 semiring varieties is described and models for the semirings
free in these varieties are given.
Received April 22, 2004; accepted in final form June 3, 2005. 相似文献
18.
Certain congruences on E-inversive E-semigroups 总被引:10,自引:0,他引:10
A semigroup S is called E-inversive if for every a ∈ S there exists x ∈ S such that ax is idempotent. S is called E-semigroup if the set of idempotents of S forms a subsemigroup. In this paper some special congruences on E-inversive E-semigroups are investigated, such as the least
group congruence, a certain semilattice congruence, some regular congruences and a certain idempotent-separating congruence. 相似文献
19.
RICRL denotes the variety of commutative residuated lattices which have an idempotent monoid operation and are representable in
the sense that they are subdirect products of linearly ordered algebras. It is shown that the subvariety lattice of RICRL is countable, despite its complexity and in contrast to several varieties of closely related algebras. 相似文献
20.
David Stanovský 《Czechoslovak Mathematical Journal》2007,57(1):191-200
We investigate the variety of residuated lattices with a commutative and idempotent monoid reduct. 相似文献