Coextensions of regular semigroups by rectangular bands. II

Meakin, John; Nambooripad, K. S. S.

doi:10.1090/S0002-9947-1982-0662053-9

Coextensions of regular semigroups by rectangular bands. II
HTML articles powered by AMS MathViewer

by John Meakin and K. S. S. Nambooripad

Trans. Amer. Math. Soc. 272 (1982), 555-568

DOI: https://doi.org/10.1090/S0002-9947-1982-0662053-9

PDF | Request permission

Abstract:

A construction of all coextensions of a regular semigroup $S$ by rectangular bands is obtained. The construction is analogous to Hall’s construction of orthodox semigroups as spined products of bands and inverse semigroups and reduces to that construction when $S$ is inverse. The results are specialized to provide a construction of the category of all normal coextensions of a regular semigroup.

References

The algebraic theory of semigroups

Pierre Antoine Grillet, The structure of regular semigroups. I. A representation, Semigroup Forum 8 (1974), no. 2, 177–183. MR 382495, DOI 10.1007/BF02194760
T. E. Hall, Orthodox semigroups, Pacific J. Math. 39 (1971), 677–686. MR 306370
T. E. Hall, Congruences and Green’s relations on regular semigroups, Glasgow Math. J. 13 (1972), 167–175. MR 318356, DOI 10.1017/S0017089500001610
John Meakin and K. S. S. Nambooripad, Coextensions of regular semigroups by rectangular bands. I, Trans. Amer. Math. Soc. 269 (1982), no. 1, 197–224. MR 637035, DOI 10.1090/S0002-9947-1982-0637035-3
K. S. S. Nambooripad, Structure of regular semigroups. I, Mem. Amer. Math. Soc. 22 (1979), no. 224, vii+119. MR 546362, DOI 10.1090/memo/0224
K. S. S. Nambooripad, Relations between cross-connections and biordered sets, Semigroup Forum 16 (1978), no. 1, 67–81. MR 486245, DOI 10.1007/BF02194614
N. R. Reilly and H. E. Scheiblich, Congruences on regular semigroups, Pacific J. Math. 23 (1967), 349–360. MR 219646
Miyuki Yamada, Regular semi-groups whose idempotents satisfy permutation identities, Pacific J. Math. 21 (1967), 371–392. MR 227302