Kernel and Trace Operators for Extensions of Brandt Semigroups期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

首页 | 本学科首页

官方微博 | 高级检索

按检索

Kernel and Trace Operators for Extensions of Brandt Semigroups

Authors:

Mario Petrich

Institution:

(1) 21420 Bol, Brac, Croatia

Abstract:

Let S be an (ideal) extension of a Brandt semigroup S₀ by a Brandt semigroup S₁ and let $\mathcal{C}(S)$ denote the congruence lattice of S. For $\rho \in \mathcal{C}(S),$ denote by $\rho _K$ and $\rho ^K$ the least and the greatest congruences on S with the same kernel as $\rho ,$ respectively, and let $\rho _T$ and $\rho ^T$ have the analogous meaning relative to trace. We establish necessary and sufficient conditions on S in order that one or more of the operators

$\rho \longrightarrow \rho _K, \quad \rho \longrightarrow \rho ^K, \quad \rho \longrightarrow \rho _T, \quad \rho \longrightarrow \rho^T$

be $\vee$ - or $\wedge$ -homomorphisms on $\mathcal{C}(S).$ The conditions are expressed directly in terms of a construction of an extension of S₀ and S₁ and the proofs make use of a construction of congruences on S expressed by means of congruences on S₀ and S₁.

Keywords:

本文献已被 SpringerLink 等数据库收录！

设为首页 | 免责声明 | 关于勤云 | 加入收藏