On (*, ∼)-Green's Relations and Ortho-lc-Monoids

Abstract

An ortho-lc-monoid is a generalized orthogroup within the class of rpp semigroups. In this article, after giving some important properties of r-ample semigroups and super-r-ample semigroups, some structure theorems of ortho-lc-monoids are established, and several special cases are considered. The main techniques that we use in the study are the (*, ∼)-Green's relations and semispined product of semigroups.

Key Words:

• (*, ∼)-Green's relations
• Ortho-lc-monoids
• Semispined products
• Super-r-ample semigroups

2000 Mathematics Subject Classification:

• 20M10

ACKNOWLEDGMENTS

The authors would like to thank the referees for their valuable modifying suggestions.

The research of the first author is supported by a NSF (China) grant #10871161.

Notes

Communicated by V. Gould.