Research ArticleOpen AccessGoogle Scholar indexed
New Properties over a New Type of Wreath Products on Monoids
Department of Mathematics, Science Faculty, King Abdulaziz University, Jeddah, Saudia Arabia
- 1 Department of Mathematics, Science Faculty, King Abdulaziz University, Jeddah, Saudia Arabia
Advances in Pure Mathematics·Volume 09 (2019)·Pages 629–636·Published 30 August 2019·DOI10.4236/apm.2019.98032
Copy link · social · email
Abstract
In [1], a new consequence of the (restricted) wreath product for arbitrary monoids A and B with an underlying set . Let us denote it by . Actually, in the same reference, it has been also defined the generating and relator sets for , and then proved some finite and infinite cases about it. In this paper, by considering the product, we show Green’s relations L and R as well as we present the conditions for this product to be left cancellative, orthodox and finally left (right) inverse(s).
KeywordsWreath ProductGreen’s RelationsLeft Cancellative MonoidsOrthodox MonoidsLeft (Right) Inverse
- Wazzan, S.A., Cevik, A.S. and Ates, F. (2019) The New Derivation for Wreath Products of Monoids. Filomat.
- Howie, J.M. and Ruskuc, N. (1994) Construction and Presentations for Monoids. Communications in Algebra, 22, 6209-6224. https://doi.org/10.1080/00927879408825184
- Robertson, E.F., Ruskuc, N. and Thomson, M.R. (2002) On Finite Generation and Other Finiteness Conditions for Wreath Products of Semigroups. Communications in Algebra, 30, 3851-3873. https://doi.org/10.1081/AGB-120005823
- Baumslag, G. (1961) Wreath Products and Finitely Presented Groups. Mathematische Zeitschrift, 75, 22-28. https://doi.org/10.1007/BF01211007
- Cevik, A.S. (2000) The Efficiency of Standard Wreath Product. Proceedings of the Edinburgh Mathematical Society, 43, 415-423. https://doi.org/10.1017/S0013091500021003
- Cevik, A.S. (2003) The p-Cockcroft Property of Semi-Direct Products of Monoids. International Journal of Algebra and Computation, 13, 1-16. https://doi.org/10.1142/S0218196703001298
- Meldrum, J.D.P. (1995) Wreath Products of Groups and Semigroups. Longman, Harlow.
- Howie, J.M. (1995) Fundamentals of Semigroups Theory. Clarendon Press, Oxford.
- Lawson, M.V. (1998) Inverse Semigroups: The Theory of Partial Symmetries. World Scientific, Singapore. https://doi.org/10.1142/3645
- Saito, T. (1989) Orthodox Semidirect Products and Wreath Products of Monoids. Semigroup Forum, 38, 347-354. https://doi.org/10.1007/BF02573242
- Zhang, R. (1999) A Note on Orthodox Semidirect Products and Wreath Products of Monoids. Semigroup Forum, 58, 262-266. https://doi.org/10.1007/s002339900019
- Hickey, J.B. and Lawson, M.V. (1997) Unit Regular Monoids. Proceedings of the Edinburgh Mathematical Society, 127A, 127-144. https://doi.org/10.1017/S0308210500023532
- McFadden, R.B. (1984) Unit-Regular Orthodox Semigroups. Glasgow Mathematical Journal, 25, 229-240. https://doi.org/10.1017/S0017089500005656
- Bijev, G. and Todorov, K. (1980) Coregular Semigroups. Notes on Semigroups VI, Budapest (1980-1984), 1-11.
- Dimitrova, I. and Koppitz, J. (2011) Coregular Semigroups of Full Transformations. Demonstratio Mathematica, 44, 739-753. https://doi.org/10.1515/dema-2013-0342