The Structure of Ortho-LC-Monoids

Abstract

The super-r-wide semigroups (in [6], called super-r-ample semigroups) [ortho-lc-monoids] within the class of rpp semigroups form a kind of generalized completely regular semigroups [orthogroups]. In this article, some structure theorems of ortho-lc-monoids are established and some special ortho-lc-monoids such as orthocrypto-lc-monoids, lc-Clifford semigroups, which we defined, are considered; the semilattice decomposition of super-r-wide semigroups is given. As direct corollaries of the results that we obtained, some new structure theorems for ortho-c-monoids and orthogroups, different from [10, 13], are given, and hence, the structure theorem for ortho-lc-monoids that we established is not the direct generalization of the results in [10, 13]; the structure of orthocryptogroups is reobtained; the well-known Clifford theorem is further generalized.

Key Words:

• Ortho-lc-monoids
• Orthocrypto-lc-monoids
• Super-r-wide semigroups

2000 Mathematics Subject Classification:

• 20M10

ACKNOWLEDGEMENTS

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

The research is supported by a grant of National Natural Science Foundation of China (Grant No: 10871161, 10971160, and 11101336), Natural Science Foundation Project of CQ CSTC2009BB2291, the talents technology fund of Xi'an University of Architecture and Technology (Grant No: RC1015).

Notes

Communicated by V. Gould.