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Uniform Bands

  • Justin Albert (a1) and Francis Pastijn (a1)
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.

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1.Broeksteeg, R., A concept of variety for regular biordered sets, Semigroup Forum 49 (1994), 335348.
2.Clifford, A. H. and Preston, G. B., The algebraic theory of semigroups, I (American Mathematical Society, Providence, RI, 1961).
3.Clifford, A. H. and Preston, G. B., The algebraic theory ofsemigroups, II (American Mathematical Society, Providence, RI, 1967).
4.Feigenbaum, R., Regular semigroup congruences, Semigroup Forum 17 (1979), 373377.
5.Gerhard, J. A., Free completely regular semigroups, I, J. Alg. 82 (1983), 135142.
6.Gerhard, J. A., Free completely regular semigroups, II, J. Alg. 82 (1983), 143156.
7.Grätzer, G., Universal algebra (Springer, 1979).
8.Hall, T. E., On regular semigroups whose idempotents form a subsemigroup, Bull. Austral. Math. Soc. 1 (1969), 195208.
9.Hall, T. E., On orthodox semigroups and uniform and anti-uniform bands, J. Alg. 16 (1970), 204217.
10.Hall, T. E., On regular semigroups whose idempotents form a subsemigroup: addenda, Bull. Austral. Math. Soc. 3 (1970), 287288.
11.Hall, T. E., Orthodox semigroups, Pac. J. Math. 39 (1971), 677686.
12.Hall, T. E., On regular semigroups, J. Alg. 24 (1973), 124.
13.Howie, J. M., An introduction to semigroup theory, London Mathematical Society Monographs, Volume 7 (Academic, 1976).
14.Howie, J. M., Fundamentals of semigroup theory, London Mathematical Society Monographs, Volume 12 (Clarendon, Oxford, 1995).
15.Kadourek, J. and Polák, L., On the word problem for free completely regular semigroups, Semigroup Forum 34 (1986), 127138.
16.Leemans, H. and Pastijn, F., Embedding inverse semigroups in bisimple congruence-free inverse semigroups, Q. J. Math. (2) 34 (1983), 455458.
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).
18.Nambooripad, K. S. S., Pseudosemilattices and biordered sets, I, Bull. Belg. Math. Soc. Simon Stevin 55 (1981), 103110.
19.Oliveira, L., Varieties of pseudosemilattices, PhD thesis, Marquette University, Milwaukee (2004).
20.Pastijn, F., Uniform lattices, Acta Sci. Math. (Szeged) 42 (1980), 305311.
21.Pastijn, F., Congruences on regular semigroups: a survey, in Proceedings of the 1984 Marquette conference on semigroups, pp. 159175 (Marquette University, Milwaukee, 1984).
22.Pastijn, F., The idempotents in a periodic semigroup, Int. J. Alg. Comput. 6 (1996), 511540.
23.Pastijn, F. J. and Petrich, M., Regular semigroups as extensions, Research Notes in Mathematics, Volume 136 (Pitman, Boston, MA, 1985).
24.Pastijn, F. and Petrich, M., Congruences on regular semigroups, Trans. Am. Math. Soc. 295 (1986), 607633.
25.Petrich, M., Lectures in semigroups (Wiley, 1977).
26.Płonka, J., On a method of construction of abstract algebras, Fund. Math. LXI (1967), 183189.
27.Plonka, J., Sums of direct systems of abstract algebras, Bull. Polish Acad. Sci. Math. XV(3) (1967), 133135.
28.Preston, G. B., Embedding any semigroup in a D-simple semigroup, Trans. Am. Math. Soc. 93 (1959), 351355.
29.Reilly, N. R., Embedding inverse semigroups in bisimple inverse semigroups, Q. J. Math. (2) 16 (1965), 183187.
30.Trotter, P. G., Free completely regular semigroups, Glasgow Math. J. 25 (1984), 241254.
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Proceedings of the Edinburgh Mathematical Society
  • ISSN: 0013-0915
  • EISSN: 1464-3839
  • URL: /core/journals/proceedings-of-the-edinburgh-mathematical-society
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