Semilattice transversals of regular bands I

Every regular band can be isomorphically embedded into a regular band which has a semilattice transversal. The latter constitute the variety of regular split bands, whose subvariety lattice is isomorphic to the lattice of regular band varieties.     

半格分次弱Hopf代数的$G$-Cleft扩张

本文首先将Clifford幺半群代数分解为交叉积的半格直和,然后将这个结果通过$H$-$G$-cleft扩张推广到所谓的$G$-交叉积上.     

Rank properties of certain semigroups

In this paper we consider certain ranks of some semigroups. These ranks are r ₁(S),r ₂(S),r ₃(S),r ₄(S) and r ₅(S) as defined below. We have r ₁≤r ₂≤r ₃≤r ₄≤r ₅. The semigroups are CL _n ,CL _m ×CL _n ,Z _n and SL _n . Here CL _n is a chain with n elements, Z _n is the zero semigroup on n elements and SL _n is the free semilattice generated by n elements and having 2 ⁿ −1 elements. We find many of the ranks for these classes of semigroups.     

$G$-交叉积在$G$-inner作用下的等价刻画

本文给出两个具有相同半格$Y$ 的半格分次弱Hopf代数的$G$-inner 作用的定义, 然后给出两个$G$-交叉积同构的充分必要条件.     

左C-半群的左交错积结构

给出了左C-半群的另一种结构,所谓左交错积结构,并刻画了它的特殊情形.这种结构为左C-半群在广义正则半群类中的再推广奠定了基础.     

Representations of distributive semilattices in ideal lattices of various algebraic structures

We study the relationships among existing results about representations of distributive semilattices by ideals in dimension groups, von Neumann regular rings, C*-algebras, and complemented modular lattices. We prove additional representation results which exhibit further connections with the scattered literature on these different topics. Received March 2, 1998; accepted in final form November 9, 2000.     

关于蕴涵BCK—代数的伴随半群

我们证明了蕴涵BCK-代数的伴随半群是一个上半格;具有条件（s)的蕴涵BCK-代数的伴随半群是一个广义布尔代数。更进一步证明了有界蕴涵BCK-代数的伴随半群是一个布尔代数。     

毕竟PI—强rpp半群

定义了毕竟PI-强rpp半群,并刻划了这类半群的结构。     

The Closed Subsemigroups of a Clifford Semigroup

In this paper we study the closed subsemigroups of a Clifford semigroup. It is shown that {∪α∈Y′ Gα | Y′∈ P(Y) } is the set of all closed subsemigroups of a Clifford semigroup S = [Y; Gα; ?α, β], where Y′denotes the subsemilattice of Y generated by Y′. In particular, G is the only closed subsemigroup of itself for a group G and each one of subsemilattices of a semilattice is closed. Also, it is shown that the semiring P(S) is isomorphic to the semiring P(Y) for a Clifford semigroup S = [Y; Gα; ?α, β].     

矩阵逆半群

讨论矩阵逆半群的一些基本性质, 证明矩阵逆半群的幂等元集是有限布尔格的子半格, 从而证明等秩矩阵逆半群是群, 然后完全确定二级矩阵逆半群的结构：一个二级矩阵逆半群或者同构于二级线性群,或者同构于二级线性群添加一个零元素,或者是交换线性群的有限半格, 或者满足其他一些性质; 对于由某些二级矩阵构成的集合, 我们给出了它们成为矩阵逆半群的充分必要条件.