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1.
半群代数中理想FA良序基的构造   总被引:6,自引:0,他引:6  
刘卫江  冯果忱 《数学研究》2001,34(3):256-263
讨论了在半群代数k[A]中,如何利用Gause-Jordan消元法去构造半群代数的理想的良序基,进而得到理想的良性基-Groedner-基。  相似文献
2.
This paper explores several applications of Möbius functions to the representation theory of finite semigroups. We extend Solomon's approach to the semigroup algebra of a finite semilattice via Möbius functions to arbitrary finite inverse semigroups. This allows us to explicitly calculate the orthogonal central idempotents decomposing an inverse semigroup algebra into a direct product of matrix algebras over group rings. We also extend work of Bidigare, Hanlon, Rockmore and Brown on calculating eigenvalues of random walks associated to certain classes of finite semigroups; again Möbius functions play an important role.  相似文献
3.
刘卫江  冯果忱 《数学杂志》2005,25(5):499-506
本文以矩阵变换和整理论为工具,研究了在环面同态作用下零维理想的性质,证明了零维理想的环面同态矩阵是满秩的,并且刻画了零维理想在环面作用下的对应关系.  相似文献
4.
本文先给出Fuzy半群中极小Fuzy理想的一些代数性质,进而利用极小Fuzy理想刻划Fuzzy单半群的一些代数性质  相似文献
5.
Let G be a finite group acting by automorphism on a lattice A, and hence on the group algebra S=k[A]. The algebra of G-invariants in S is called an algebra of multiplicative invariants. We present an explicit version of a result of Farkas stating that multiplicative invariants of finite reflection groups are semigroup algebras.  相似文献
6.
We describe Noetherian semigroup algebras K[S] of submonoids S of polycyclic-by-finite groups over a field K. As an application, we show that these algebras are finitely presented and also that they are Jacobson rings. Next we show that every prime ideal P of K[S] is strongly related to a prime ideal of the group algebra of a subgroup of the quotient group of S via a generalised matrix ring structure on K[S]/P. Applications to the classical Krull dimension, prime spectrum, and irreducible K[S]-modules are given.  相似文献
7.
8.
A partial abelian semigroup (PAS) is a structure , where is a partial binary operation on L with domain , which is commutative and associative (whenever the corresponding elements exist). A class of congruences on partial abelian semigroups are studied such that the corresponding quotient is again a PAS. If M is a subset of a PAS L, we say that are perspective with respect to M, if there is such that and A subset M is called weakly algebraic if perspectivity with respect to M is a congruence. Some conditions are shown under which a congruence coincides with a perspectivity with respect to an appropriate set M. Especially, conditions under which the corresponding quotient is a D-poset are found. It is also shown that every congruence of MV-algebras and orthomodular lattices is given by a perspectivity with respect to an appropriate set M. Received July 17, 1995; accepted in final form September 16, 1996.  相似文献
9.
In this article, the approximate amenability of semigroup algebra ?1(S) is investigated, where (S) is a uniformly locally finite inverse semigroup. Indeed, we show that for a uniformly locally finite inverse semigroup (S), the notions of amenability, approximate amenability and bounded approximate amenability of ?1(S) are equivalent. We use this to give a direct proof of the approximate amenability of ?1(S) for a Brandt semigroup (S). Moreover, we characterize the approximate amenability of ?1(S), where S is a uniformly locally finite band semigroup.  相似文献
10.
This is the first of a series of papers in which we initiate and develop the theory of reflection monoids, motivated by the theory of reflection groups. The main results identify a number of important inverse semigroups as reflection monoids, introduce new examples, and determine their orders.  相似文献
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