No Access

STRONGLY TORSION FREE ACTS OVER MONOIDS

Abas Zare

Department of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran

Search for more papers by this author

Akbar Golchin

Department of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran

Search for more papers by this author

, and

Hossein Mohammadzadeh

Department of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran

Search for more papers by this author

https://doi.org/10.1142/S1793557113500496Cited by:3 (Source: Crossref)

Abstract

An act A_S is called torsion free if for any a, b ∈ A_S and for any right cancellable element c ∈ S the equality ac = bc implies a = b. In [M. Satyanarayana, Quasi- and weakly-injective S-system, Math. Nachr.71 (1976) 183–190], torsion freeness is considered in a much stronger sense which we call in this paper strong torsion freeness and will characterize monoids by this property of their (cyclic, monocyclic, Rees factor) acts.

Keywords:

AMSC: 20M30

References

S. Bulman-Fleming, M. Kilp and V. Laan, Comm. Algebra 29(2), 851 (2001). Crossref, Web of Science, Google Scholar
A. Golchin and H. Mohammadzadeh, J. Sci. Islam. Repub. Iran 17(4), 343 (2006). Google Scholar
A. Golchin and H. Mohammadzadeh, Int. Math. Forum 2(19), 911 (2007). Crossref, Google Scholar
A. Golchin and H. Mohammadzadeh , Ital. J. Pure Appl. Math. 25 , 175 ( 2009 ) . Web of Science, Google Scholar
A. Golchin and H. Mohammadzadeh , Southeast Asian Bull. Math. 33 , 245 ( 2009 ) . Google Scholar
A. Golchin and H. Mohammadzadeh, On Condition P', Semigroup Forum, Published online: 09 October 2012 . Google Scholar
A. Golchin , H. Mohammadzadeh and P. Rezaei , Adv. Pure Math. 2 , 104 ( 2012 ) . Crossref, Google Scholar
A. Golchin and J. Renshaw, A flatness property of acts over monoids, Conf. Semigroups, University of St. Andrews (1998) pp. 72–77. Google Scholar
A. Golchin, P. Rezaei and H. Mohammadzadeh, Czechoslovak Math. J. 59(134), 595 (2009). Crossref, Web of Science, Google Scholar
J. M. Howie , Fundamentals of Semigroup Theory , London Mathematical Society Monographs ( Oxford University Press , London , 1995 ) . Crossref, Google Scholar
M. Kilp , U. Knauer and A. Mikhalev , Monoids, Acts and Categories ( Walter de Gruyter , Berlin, New York , 2000 ) . Crossref, Google Scholar
V. Laan, Pullback and flatness properties of acts, Ph. D. thesis, Tartu (1999) . Google Scholar
V. Laan, Comm. Algebra 29(2), 829 (2001). Crossref, Web of Science, Google Scholar
J. Renshaw, Semigroup Forum 61(1), 46 (2000). Crossref, Web of Science, Google Scholar