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Journals / Hacettepe Journal of Mathematics and Statistics / 2011 / Cilt: 40 - Sayı: 3

A new example of strongly $pi$ inverse monoids

Ahmet Sinan ÇEVİK
Eylem Güzel KARPUZ
Pages
461–468
Publication Date
2022-10-18
DOI
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Since this is a new product and there are so many algebraic properties that need to be checked for it, in this paper we determine necessary and sufficient conditions for this new version to be strongly $pi$-inverse, and then give some results.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In [1], Ate¸s defined the semidirect product version of the Schützenberger product for any two monoids, and examined its regularity.
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Key Findings & Data:In [1], Ate¸s defined the semidirect product version of the Schützenberger product for any two monoids, and examined its regularity.
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Conclusion & Impact:Since this is a new product and there are so many algebraic properties that need to be checked for it, in this paper we determine necessary and sufficient conditions for this new version to be strongly $pi$-inverse, and then give some results.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

In [1], Ate¸s defined the semidirect product version of the Schützenberger product for any two monoids, and examined its regularity. Since this is a new product and there are so many algebraic properties that need to be checked for it, in this paper we determine necessary and sufficient conditions for this new version to be strongly $pi$-inverse, and then give some results.

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Cite This Article

ÇEVİK, A. S., KARPUZ, E. G. (2022). A new example of strongly $pi$ inverse monoids. Hacettepe Journal of Mathematics and Statistics, Cilt: 40 - Sayı: 3, 461–468. https://ajindex.com/articles/530610

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References (1)

  1. Ateş, F. Some new monoid and group constructions under semidirect products, Ars Comb. 91, 203-218, 2009. [2]Çevik, A. S. The p-Cockcroft property of the semidirect products of monoids, Int. Journal of Algebra and Comp. 13 (1), 1-16, 2003. [3]Clifford, A. H. and Preston, G. B. The algebraic theory of semigroups, I-II, (Mathematical Surveys 7, American Mathematical Society, 1964-1967). [4]Howie, J. M. Fundamentals of semigroup theory (Clarendon Press, Oxford, 1995). [5]Howie, J. M. and Ruskuc, N. Constructions and presentations for monoids, Comm. Algebra 22(15), 6209-6224, 1994. [6]Meldrum, J.D.P. Wreath products of groups and semigroups (Longman, Harlow, 1995). [7]Nico, W. R. On the regularity of semidirect products, J. Algebra 80, 29-36, 1983. [8]Saito, T. Orthodox semidirect products and wreath products of monoids, Semigroup Forum 38, 347-354, 1989. [9]Zhang, Y., Li, S. and Wang, D. Semidirect products and wreath products of strongly ir-inverse monoids, Georgian Math. Journal 3 (3), 293-300, 1996.