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 (2023): 0.6

SJR (2023): 0.214

SNIP (2023): 0.604

Index Copernicus (2022): 121.02

H-Index: 5

Discussiones Mathematicae - General Algebra and Applications

Article in press

Authors:

J. Brandão

João Brandão

Universidade do Algarve, Faro

email: jbrandao@ualg.pt

0000-0003-3047-7793

M. Borralho

Maria Borralho

Universidade do Algarve, Faro

email: mfborralho@ualg.pt

0000-0003-0136-3201

Title:

On the varieties $\mathcal{V}_n$

PDF

Source:

Discussiones Mathematicae - General Algebra and Applications

Received: 2023-06-16 , Revised: 2023-11-16 , Accepted: 2023-11-17 , Available online: 2024-09-11 , https://doi.org/10.7151/dmgaa.1464

Abstract:

Here we set forth the varieties $\mathcal{V}_n$ and their connection with the varieties $\mathcal{E}_n$ of epigroups. A new congruence, $akin$, which relates similar elements in a semigroup, is introduced and used to reduce epigroups keeping their subgroup structure. We devise a recipe to study the conditions for these processes.

Primary keywords:

semigroups, epigroups

Secondary keywords:

varieties, congruences

References:

  1. J. Araújo, M. Kinyon, J. Konieczny, and A. Malheiro. \newblock Four notions of conjugacy for abstract semigroups. \newblock Proceedings of the Royal Society of Edinburgh Section A: Mathematics, 147(6):1169–1214, 2017. \newblock DOI: 10.1017/S0308210517000099
  2. M. Borralho and M. Kinyon. \newblock Variants of epigroups and primary conjugacy. \newblock Communications in Algebra, 48(12):5465–5473, 2020. \newblock DOI: 10.1080/00927872.2020.1791145
  3. J. M. Howie. \newblock Fundamentals of semigroup theory. \newblock Number 12 in London Mathematical Society Monographs New Series. Oxford University Press, 1995. \newblock ISBN 0-19-851194-9
  4. W. D. Munn. \newblock Pseudo-inverses in semigroups. \newblock Mathematical Proceedings of the Cambridge Philosophical Society, 57(2):247–250, 1961. \newblock DOI: 10.1017/S0305004100035143
  5. M. Petrich and N. R. Reilly. \newblock Completely regular semigroups, volume 27. \newblock John Wiley & Sons, 1999. \newblock ISBN 10: 0471195715
  6. L. N. Shevrin. \newblock On the theory of epigroups. i. \newblock Matematicheskii Sbornik, 185(8):129–160, 1994. \newblock DOI: 10.1070/SM1995v082n02ABEH003577
  7. L. N. Shevrin. \newblock Epigroups. \newblock In Structural theory of automata, semigroups, and universal algebra, pages 331–380. Springer, 2005. \newblock DOI: 10.1007/1-4020-3817-8\_12
Close