Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Semigroups with midunits


Author: Janet E. Ault
Journal: Trans. Amer. Math. Soc. 190 (1974), 375-384
MSC: Primary 20M10
DOI: https://doi.org/10.1090/S0002-9947-1974-0340456-5
MathSciNet review: 0340456
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: A semigroup has a midunit u if $ aub = ab$ for all a and b. It is the purpose of this paper to explore semigroups with midunits, and to find an analog to the group of units. In addition, two constructions will be given which produce some semigroups with midunits, and an abstract characterization will be made of certain of these semigroups.


References [Enhancements On Off] (What's this?)

  • [1] M. R. Brown, D. W. Hardy and R. J. Painter, An embedding theorem for weakly inverse semigroups, Semigroup Forum 2 (1971), no. 4, 332-335. MR 44 #338. MR 0283105 (44:338)
  • [2] 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)
  • [3] T. E. Hall, On regular semigroups whose idempotents form a subsemigroup, Bull. Austral. Math. Soc. 1 (1969), 195-208. MR 40 #2772. MR 0249527 (40:2772)
  • [4] B. P. Kočin, The structure of inverse ideal-simple $ \omega $-semigroups, Vestnik Leningrad. Univ. 23 (1968), no. 7, 41-50. (Russian) MR 37 #2881. MR 0227296 (37:2881)
  • [5] Gerard Lallement and Mario Petrich, A generalization of the Rees theorem in semigroups, Acta Sci. Math. (Szeged) 30 (1969), 113-132. MR 39 #2899. MR 0241559 (39:2899)
  • [6] W. D. Munn, On simple inverse semigroups, Semigroup Forum 1 (1970), no. 1, 63-74. MR 41 #8553. MR 0263954 (41:8553)
  • [7] Mario Petrich, Introduction to semigroups, Charles E. Merrill Co., Columbus, Ohio, 1973. MR 0393206 (52:14016)
  • [8] -, The translational hull in semigroups and rings, Semigroup Forum 1 (1970), no. 4, 283-360. MR 42 #1919. MR 0267017 (42:1919)
  • [9] N. R. Reilly, Bisimple $ \omega $-semigroups, Proc. Glasgow Math. Assoc. 7 (1966), 160-167. MR 32 #7665. MR 0190252 (32:7665)
  • [10] R. J. Warne, Direct decomposition of regular semigroups, Proc. Amer. Math. Soc. 19 (1968), 1155-1158. MR 38 #258. MR 0231932 (38:258)
  • [11] Miyuki Yamada, A note on middle unitary semigroups, Kōdai Math. Sem. Rep. 7 (1955), 49-52. MR 17, 585. MR 0074429 (17:585a)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 20M10

Retrieve articles in all journals with MSC: 20M10


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1974-0340456-5
Keywords: Midunit, regular semigroup, semigroup of midunits, Bruck-Reilly extension, rectangular group, rectangular semigroup
Article copyright: © Copyright 1974 American Mathematical Society

American Mathematical Society