It is known that a C-rpp semigroup can be described as a strongsemilattice of left cancellative monoids. In this paper, weintroduce the class of left C-wrpp semigroups which includes theclass of left C-rpp semigroups as a subclass. We shallparticularly show that the semi-spined product of a left regularband and a C-wrpp semigroup forms a curler which is a leftC-wrpp semigroup and vice versa. Results obtained by Fountainand Tang on C-wrpp semigroups are extended and strengthened.
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J.B. Fountain (1977) ArticleTitleRight pp monoidswith central idempotents Semigroup Forum 13 229–237 Occurrence Handle430110 Occurrence Handle0353.20051 Occurrence Handle10.1007/BF02194941
J.B. Fountain (1982) ArticleTitleAbundant semigroups Proc.London Math. Soc. 44 IssueID3 103–123 Occurrence Handle642795 Occurrence Handle0481.20036 Occurrence Handle10.1112/plms/s3-44.1.103
Y.Q. Guo K.P. Shum P.Y. Zhu (1995) ArticleTitleThe structure of leftC–rpp semigroups Semigroup Forum 50 9–23 Occurrence Handle1301549 Occurrence Handle0821.20046 Occurrence Handle10.1007/BF02573502
Y.Q. Guo (1996) ArticleTitleStructure of weakly left C-semigroups Chinese Sci. Bull. 41 462–467 Occurrence Handle1399389 Occurrence Handle0856.20040
Guo, X.J., Y.Q. Guo and K.P. Shum, Semi-spined productstructure of left C-a semigroups, “Papers from theInternational Conference on Semigroups and its Related Topics held atYunnan University, Kunming, August 1995” (K.P. Shum, Y. Guo, M.Ito and Y. Fong, editors),Springer-Verlag, Singapore, 1998, 157–166
X.J. Guo K.P. Shum Y.Q. Guo (2001) ArticleTitlePerfectC–rpp semigroups Comm. Algebra 29 2447–2459 Occurrence Handle1845122 Occurrence Handle0989.20048 Occurrence Handle10.1081/AGB-100002400
Howie, J.M., An Introduction to Semigroup Theory,Academic Press, London, 1976
N. Kimura (1958) ArticleTitleThe structure of idempotent semigroups II Pacific J. Math 8 257–275 Occurrence Handle102563 Occurrence Handle0084.02702
Petrich, M., Lectures in Semigroups, AkademieVerlag, Berlin, 1977
X.M. Ren K.P. Shum (2000) ArticleTitleStructuretheorem for right pp semigroups with left central idempotents Discuss. Math. Gen. Algebra Appl. 20 63–75 Occurrence Handle1782086 Occurrence Handle0966.20027
X.M. Ren K.P. Shum (1999) ArticleTitleAbundantsemigroups with left central idempotents Pure Math. Appl. 10 109–113 Occurrence Handle1721945 Occurrence Handle0938.20047
X.M. Ren K.P. Shum Y.Q. Guo (1997) ArticleTitleOn spinedproduct of quasi-rectangular groups Algebra Colloq. 4 IssueID2 187–194 Occurrence Handle1682741 Occurrence Handle0887.20027
M. Satyayarana (1973) ArticleTitleOn Left CancellativeSemigroups Semigroup Forum 6 317–329 Occurrence Handle376923 Occurrence Handle10.1007/BF02389139
Shum, K.P. and Y.Q. Guo, Regular semigroup andtheir generalizations, “Rings, Groups and Algebras”, Lecture NotesSeries in Pure and Applied Math., vol. 181, Dekker, New York, 1996,181–226
X.D. Tang (1997) ArticleTitleOn a theorem of C–wrpp semigroups Comm. Algebra 25 1499–1504 Occurrence Handle1444014 Occurrence Handle0879.20030 Occurrence Handle10.1080/00927879708825931
P.Y. Zhu Y.Q. Guo K.P. Shum (1992) ArticleTitleStructureand characterizations of left Clifford semigroups Sci.China, Ser. A 35 791–805 Occurrence Handle1196631 Occurrence Handle0781.20035
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Communicated by J.B. Fountain
The research of the first author is supported by a postdoctoral fellowship of Chengzhou University, China. The research of the second author is partially supported by a UGC (HK) earmarked grant #2160176 (2001/2003).
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Du, L., Shum, K.P. On left C-wrpp semigroups. Semigroup Forum 67, 373–387 (2003). https://doi.org/10.1007/s00233-001-0006-9
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DOI: https://doi.org/10.1007/s00233-001-0006-9