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

Autor:	Sureeporn Chaopraknoi, Pongsan Prakitsri, Teeraphong Phongpattanacharoen
Rok vydání:	2014
Předmět:	Linear map Discrete mathematics Pure mathematics Semigroup General Mathematics Bounded function Special classes of semigroups Mathematics
Zdroj:	Bulletin of the Australian Mathematical Society. 91:104-115
ISSN:	1755-1633 0004-9727
DOI:	10.1017/s0004972714000793
Popis:	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.
Databáze:	OpenAIRE
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