DM-GAA

ISSN 1509-9415 (print version)

ISSN 2084-0373 (electronic version)

https://doi.org/10.7151/dmgaa

Discussiones Mathematicae - General Algebra and Applications

Cite Score: 0.4

SJR: 0.203

SNIP: 0.562

MCQ: 0.12

Index Copernicus: 121.02

Discussiones Mathematicae - General Algebra and Applications

Article in press


Authors:

A. Nagy

Attila Nagy

Institute of Mathematics
Department of Algebra
Budapest University of Technology and Economics
Műegyetem rkp. 3., Budapest, 1111 Hungary

email: nagyat@math.bme.hu

Title:

A construction of semigroups containing middle units

PDF

Source:

Discussiones Mathematicae - General Algebra and Applications

Accepted: 2023-12-14 , Available online: 2023-12-14 , https://doi.org/10.7151/dmgaa.1448

Abstract:

In this paper, we show that semigroups containing middle units can be constructed from semigroups containing one-sided identity elements. Moreover, we show that regular semigroups containing middle units can be obtained from regular monoids.

Keywords:

semigroup, regular semigroup, middle unit

References:

  1. J.E. Ault, Semigroups with midunits, Semigroup Forum 6 (1973) 346–351.
    https://doi.org/10.1007/BF02389143
  2. J.E. Ault, Semigroups with midunits, Trans. Amer. Math. Soc. 190 (1974) 375–384.
    https://doi.org/10.1090/S0002-9947-1974-0340456-5
  3. T.S. Blyth, On middle units in orthodox semigroups, Semigroup Forum 13-1 (1976) 261–265.
    https://doi.org/10.1007/BF02194944
  4. T.S. Blyth and R. McFadden, On the construction of a class of regular semigroups, J. Algebra 81 (1983) 1–22.
    https://doi.org/10.1016/0021-8693(83)90205-3
  5. J.L. Chrislock, Semigroups whose regular representation is a group, Proc. Japan Acad. 40 (1964) 799–800.
    https://doi.org/10.3792/pja/1195522567
  6. J.L. Chrislock, Semigroups whose regular representation is a right group, Amer. Math. Monthly 74 (1967) 1097–1100.
    https://doi.org/10.2307/2313623
  7. A.H. Clifford and G.B. Preston, The Algebraic Theory of Semigroups I, Amer. Math. Soc. (Providence R.I., 1961).
    https://doi.org/10.1090/surv/007.1
  8. J.B. Hickey, Semigroups under a sandwich operation, Proc. Edinburgh Math. Soc. 26 (1983) 371–382.
    https://doi.org/10.1017/S0013091500004442
  9. D.B. McAlister, Regular Rees matrix semigroups and regular Dubreil-Jacotin semigroups, J. Australian Math. Soc. 31 (1981) 325–336.
    https://doi.org/10.1017/S1446788700019467
  10. A. Nagy, Special Classes of Semigroups, Kluwer Academic Publishers (Dordrecht, Boston, London, 2001).
    https://doi.org/10.1007/978-1-4757-3316-7
  11. A. Nagy, Remarks on the paper "M. Kolibiar, On a construction of semigroups", Periodica Math. Hungarica 71 (2015) 261–264.
    https://doi.org/10.1007/s10998-015-0094-z
  12. A. Nagy, Left equalizer simple semigroups, Acta Math. Hungarica 148(2) (2016) 300–311.
    https://doi.org/10.1007/s10474-015-0578-6
  13. A. Nagy and O. Nagy, A construction of semigroups whose elements are middle units, Int. J. Algebra 14(3) (2020) 163–169.
    https://doi.org/10.12988/ija.2020.91248
  14. M. Petrich, Lectures in Semigroups (Akademie-Verlag-Berlin, 1977).
  15. M. Yamada, A note on middle unitary semigroups, Kodai Math. Sem. Rep. 7(1955) 49–52.
    https://doi.org/10.2996/kmj/1138843607

Close