Hostname: page-component-76fb5796d-qxdb6 Total loading time: 0 Render date: 2024-04-26T13:20:03.769Z Has data issue: false hasContentIssue false
  • English
  • Français

Uniform Bands

Published online by Cambridge University Press:  18 July 2014

Justin Albert  and
Francis Pastijn
Justin Albert
Affiliation:
Department of Mathematics, Statistics and Computer Science, Marquette University, Milwaukee, WI 53233, USA, (justin.albert@marquette.edu; francis.pastijn@marquette.edu)
Francis Pastijn
Affiliation:
Department of Mathematics, Statistics and Computer Science, Marquette University, Milwaukee, WI 53233, USA, (justin.albert@marquette.edu; francis.pastijn@marquette.edu)
Get access Rights & Permissions [Opens in a new window]

Abstract

A semigroup B in which every element is an idempotent can be embedded into such a semigroup B′, where all the local submonoids are isomorphic, and in such a way that B and B′ satisfy the same equational identities. In view of the properties preserved under this embedding, a corresponding embedding theorem is obtained for regular semigroups whose idempotents form a subsemigroup.

Keywords

banduniform bandorthodox semigroupbisimple semigroupvarietyPrimary 20M19Secondary 20M0720M1720M18
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 57 , Issue 3 , October 2014 , pp. 575 - 587
Copyright
Copyright © Edinburgh Mathematical Society 2014 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Broeksteeg, R., A concept of variety for regular biordered sets, Semigroup Forum 49 (1994), 335–348.CrossRefGoogle Scholar
2.Clifford, A. H. and Preston, G. B., The algebraic theory of semigroups, I (American Mathematical Society, Providence, RI, 1961).Google Scholar
3.Clifford, A. H. and Preston, G. B., The algebraic theory ofsemigroups, II (American Mathematical Society, Providence, RI, 1967).Google Scholar
4.Feigenbaum, R., Regular semigroup congruences, Semigroup Forum 17 (1979), 373–377.Google Scholar
5.Gerhard, J. A., Free completely regular semigroups, I, J. Alg. 82 (1983), 135–142.Google Scholar
6.Gerhard, J. A., Free completely regular semigroups, II, J. Alg. 82 (1983), 143–156.Google Scholar
7.Grätzer, G., Universal algebra (Springer, 1979).Google Scholar
8.Hall, T. E., On regular semigroups whose idempotents form a subsemigroup, Bull. Austral. Math. Soc. 1 (1969), 195–208.Google Scholar
9.Hall, T. E., On orthodox semigroups and uniform and anti-uniform bands, J. Alg. 16 (1970), 204–217.CrossRefGoogle Scholar
10.Hall, T. E., On regular semigroups whose idempotents form a subsemigroup: addenda, Bull. Austral. Math. Soc. 3 (1970), 287–288.CrossRefGoogle Scholar
11.Hall, T. E., Orthodox semigroups, Pac. J. Math. 39 (1971), 677–686.Google Scholar
12.Hall, T. E., On regular semigroups, J. Alg. 24 (1973), 1–24.Google Scholar
13.Howie, J. M., An introduction to semigroup theory, London Mathematical Society Monographs, Volume 7 (Academic, 1976).Google Scholar
14.Howie, J. M., Fundamentals of semigroup theory, London Mathematical Society Monographs, Volume 12 (Clarendon, Oxford, 1995).CrossRefGoogle Scholar
15.Kadourek, J. and Polák, L., On the word problem for free completely regular semigroups, Semigroup Forum 34 (1986), 127–138.Google Scholar
16.Leemans, H. and Pastijn, F., Embedding inverse semigroups in bisimple congruence-free inverse semigroups, Q. J. Math. (2) 34 (1983), 455–458.CrossRefGoogle Scholar
17.NAMBOORIPAD, K. S. S., Structure of regular semigroups, I, Memoirs of the American Mathematical Society, Volume 22, Number 224 (American Mathematical Society, Providence, RI, 1979).Google Scholar
18.Nambooripad, K. S. S., Pseudosemilattices and biordered sets, I, Bull. Belg. Math. Soc. Simon Stevin 55 (1981), 103–110.Google Scholar
19.Oliveira, L., Varieties of pseudosemilattices, PhD thesis, Marquette University, Milwaukee (2004).Google Scholar
20.Pastijn, F., Uniform lattices, Acta Sci. Math. (Szeged) 42 (1980), 305–311.Google Scholar
21.Pastijn, F., Congruences on regular semigroups: a survey, in Proceedings of the 1984 Marquette conference on semigroups, pp. 159–175 (Marquette University, Milwaukee, 1984).Google Scholar
22.Pastijn, F., The idempotents in a periodic semigroup, Int. J. Alg. Comput. 6 (1996), 511–540.Google Scholar
23.Pastijn, F. J. and Petrich, M., Regular semigroups as extensions, Research Notes in Mathematics, Volume 136 (Pitman, Boston, MA, 1985).Google Scholar
24.Pastijn, F. and Petrich, M., Congruences on regular semigroups, Trans. Am. Math. Soc. 295 (1986), 607–633.Google Scholar
25.Petrich, M., Lectures in semigroups (Wiley, 1977).Google Scholar
26.Płonka, J., On a method of construction of abstract algebras, Fund. Math. LXI (1967), 183–189.Google Scholar
27.Plonka, J., Sums of direct systems of abstract algebras, Bull. Polish Acad. Sci. Math. XV(3) (1967), 133–135.Google Scholar
28.Preston, G. B., Embedding any semigroup in a D-simple semigroup, Trans. Am. Math. Soc. 93 (1959), 351–355.Google Scholar
29.Reilly, N. R., Embedding inverse semigroups in bisimple inverse semigroups, Q. J. Math. (2) 16 (1965), 183–187.CrossRefGoogle Scholar
30.Trotter, P. G., Free completely regular semigroups, Glasgow Math. J. 25 (1984), 241–254.Google Scholar