有限集上变换半群的最大子半格

Semilattice Indecomposable Finite Semigroups With Large Subsemilattices

In this paper we show that if $Y$ is a subsemilattice of a finite semilattice indecomposable semigroup $S$ then $|Y|\leq 2\left\lfloor \frac{|S|-1}{4}\right\rfloor+1$. We also characterize finite semilattice indecomposable semigroups $S$ which contains a subsemilattice $Y$ with $|S|=4k+1$ and $|Y|=2\left\lfloor \frac{|S|-1}{4}\right\rfloor+1=2k+1$. They are special inverse semigroups. Our investigation is based on our new result proved in this paper which characterize finite semilattice indecomposable semigroups with a zero by only use the properties of its semigroup algebra.

独立代数自同态幺半群的最大子半格

The Largest Subsemilattices of the Endomorphism Monoid of an Independence Algebra

一个代数$\A$称为独立代数，如果它是一个拟阵代数，并且定义在$\A$的基$X$上的每个映射$\al:X\to A$都可以扩展为$\A$的自同态。这些代数是向量空间的特别好的推广，因此它们自然地出现在数学的几个分支中，如模型论，群论和半群理论。众所周知，拟阵代数有一个定义良好的维数概念。设$\A$是任意有限维独立代数$n$，至少有两个元素。用$\End(\A)$表示$\A$的自同态幺半群。证明了$\End(\A)$的最大子半格具有$2^{n-1}$元素（如果$\A$的克隆不包含任何常数运算）或$2^n$元素（如果$\A$的克隆包含常数运算）.作为推论，我们得到公式的大小最大的子半格：一些变种的幺半群的线性算子的有限维向量空间，幺半群的完整的转换有限集$X$，幺半群的部分转换$X$，幺半群的自同态的自由$G$ -集有限集的自由发电机，等等。本文结束了一个相对较大的数量的问题，可能会引起注意的专家在线性代数，环理论，极值组合，群论，半群理论，泛代数几何，和泛代数。

平衡剩余偏序半群的剩余相干化

Residual coherentization of balanced residuated partially ordered semigroups

研究平衡剩余偏序半群，通过构造剩余相干化$\mathcal C_{\mathrm r}(\mathbf M)$，给出规范分解 - 重构理论，其块定义规范分量，商骨架记录目标分量，还与子半格稳定可见性分解比较，显示前者划分更精细。

刻画特定类型的最大交换（全与部分）变换半群

Characterizing the largest commutative (full and partial) transformation semigroups of certain types

本文刻画了有限集$X$上全变换半群$\mathcal{T}(X)$和部分变换半群$\mathcal{P}(X)$的多种最大交换子半群，提供了$\mathcal{T}(X)$幂零子半群的替代确定方法，并推导了二者交换图的团数、围长和编织度。

交换幂零变换半群

Commutative nilpotent transformation semigroups

本文证明有限集合上全变换半群的交换幂零子半群的最大阶数等于零子半群的最大阶数，且最大交换幂零子半群即 Cameron 等人刻画的零半群。

Varieties of Boolean inverse semigroups

In an earlier work, the author observed that Boolean inverse semi-groups, with semigroup homomorphisms preserving finite orthogonal joins, form a congruence-permutable variety of algebras, called biases. We give a full description of varieties of biases in terms of varieties of groups: (1) Every free bias is residually finite. In particular, the word problem for free biases is decidable. (2) Every proper variety of biases contains a largest finite symmetric inverse semigroup, and it is generated by its members that are generalized rook matrices over groups with zero. (3) There is an order-pres…