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Abstract
The aim of this paper is to study a class of rpp semigroups, namely the perfect rpp semigroups. We obtain some characterization theorems for such semigroups. In particular, the spined product structure of perfect rpp semigroups is established. As an application of spined product structure, we prove that a perfect rpp semigroup is a strong semilattice of left cancellative planks. By a left cancellative plank, we mean a product of a left cancellative monoid and a rectangular band. Thus, the work of J.B. Fountain on C-rpp semigroups is further developed.
*The research of the first author is supported by the Natural Science Foundation and the Education Committee Foundation of Yunnan Province, China and also by the Foundation of Yunnan Province, China.
#The research of the second author is partially supported by UGC grant (Hong Kong) #2260126.
†The research of the third author is supported by a grant of NSF, China and a grant from the Basic Science Research Council of Yunnan Province, China.
ACKNOWLEDGMENT
The authors would like to thank the referee for his valuable comments and suggestions. He helped to shape the paper in its present form.
Notes
*The research of the first author is supported by the Natural Science Foundation and the Education Committee Foundation of Yunnan Province, China and also by the Foundation of Yunnan Province, China.
#The research of the second author is partially supported by UGC grant (Hong Kong) #2260126.
†The research of the third author is supported by a grant of NSF, China and a grant from the Basic Science Research Council of Yunnan Province, China.