THE NATURAL PARTIAL ORDER ON LINEAR SEMIGROUPS WITH NULLITY AND CO-RANK BOUNDED BELOW

被引：3

作者：

Chaopraknoi, Sureeporn ^{[1
]}

Phongpattanacharoen, Teeraphong ^{[1
]}

Prakitsri, Pongsan ^{[1
]}

机构：

[1] Chulalongkorn Univ, Dept Math & Comp Sci, Fac Sci, Bangkok 10330, Thailand

来源：

BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY | 2015年 / 91卷 / 01期

关键词：

linear transformation semigroup; natural partial order; left (right) compatible element; minimal (maximal) element; TRANSFORMATION SEMIGROUPS;

D O I：

10.1017/S0004972714000793

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Higgins ['The Mitsch order on a semigroup', Semigroup Forum 49 (1994), 261-266] showed that the natural partial orders on a semigroup and its regular subsemigroups coincide. This is why we are interested in the study of the natural partial order on nonregular semigroups. Of particular interest are the nonregular semigroups of linear transformations with lower bounds on the nullity or the co-rank. In this paper, we determine when they exist, characterise the natural partial order on these nonregular semigroups and consider questions of compatibility, minimality and maximality. In addition, we provide many examples associated with our results.

引用

页码：104 / 115

页数：12

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