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On the structure of semigroups which are unions of groups
Author:
R. J. Warne
Journal:
Trans. Amer. Math. Soc. 186 (1973), 385-401
MSC:
Primary 20M10
MathSciNet review:
0333049
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Additional Information
Abstract: We characterize semigroups S which are unions of groups as generalized Schreier products of groups, semilattices of right zero semigroups, and semilattices of left zero semigroups. We then give several specializations of this result utilizing Schreier products, semidirect products, and direct products.
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J. Warne, 𝐿-unipotent semigroups, Nigerian J. Sci.
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J. Warne, Generalized
\𝑐𝑎𝑙𝐿-unipotent semigroups, Boll. Un.
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J. Warne, Bands of maximal left groups, Rev. Roumaine Math.
Pures Appl. 17 (1972), 1705–1707. MR 0318366
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Yamada, Strictly inversive semigroups, Bull. Shimane Univ.
Natur. Sci. 13 (1963), 128–138 (1964). MR 0393307
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Yamada, Construction of inversive semigroups, Mem. Fac. Lit.
Sci. Shimane Univ. Natur. Sci. 4 (1971), 1–9. MR 0352311
(50 #4798)
- [1]
- Gordon L. Bailes, Right inverse semigroups, Semigroup Forum (to appear).
- [2]
- A. H. Clifford, Semigroups admitting relative inverses, Ann. of Math (2) 42 (1941), 1037-1049. MR 3, 199. MR 0005744 (3:199c)
- [3]
- A. H. Clifford and G. B. Preston, The algebraic theory of semigroups. Vol. I, Math. Surveys, no. 7, Amer. Math. Soc., Providence, R. I., 1961. MR 24 #A2627. MR 0132791 (24:A2627)
- [4]
- A. H. Clifford, The structure of orthodox unions of groups, Semigroup Forum 3 (1972), 283-337. MR 0301117 (46:275)
- [5]
- Naoki Kimura, Note on idempotent semigroups. I, Proc. Japan Acad. 33 (1957), 642-645. MR 20 #4602. MR 0098140 (20:4602)
- [6]
- M. Petrich, Topics in semigroups, Lecture Notes, Pennsylvania State University, 1967, 534 pp.
- [7]
- D. Rees, On semigroups, Proc. Cambridge Philos. Soc. 36 (1940), 387-400. MR 2, 127. MR 0002893 (2:127g)
- [8]
- R. J. Warne,
 -unipotent semigroups, Nigerian J. Sci. 5 (1972), 245-248. MR 0344371 (49:9110)
- [9]
- -, Generalized
 -unipotent semigroups, Bol. Un. Mat. Ital. 5 (1972), 43-47. MR 0308307 (46:7421)
- [10]
- -, On the structure of idempotent semigroups, Proc. Amer. Math. Soc. 37 (1973), 17-21. MR 0306380 (46:5506)
- [11]
- -, Bands of maximal left groups, Rev. Roumaine Math. Pures Appl. 27 (1972), 1705-1707. MR 0318366 (47:6913)
- [12]
- M. Yamada, Strictly inversive semigroups, Bull. Shimane Univ. Nat. Sci. 13 (1964), 128-138. MR 0393307 (52:14117)
- [13]
- -, Construction of inversive semigroups, Mem. Fac. Lit. Sci. Shimane Univ. Natur. Sci. 4 (1971), 1-9. MR 0352311 (50:4798)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S0002-9947-1973-0333049-6
PII:
S 0002-9947(1973)0333049-6
Keywords:
Union of groups,
Schreier product,
semidirect product,
spined product,
semilattice of right zero semigroups
Article copyright:
© Copyright 1973 American Mathematical Society
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