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REVERSIBLE SKEW GENERALIZED POWER SERIES RINGS

Part of: Rings and algebras arising under various constructions Conditions on elements

Published online by Cambridge University Press:  21 July 2011

A. R. NASR-ISFAHANI
A. R. NASR-ISFAHANI*
Affiliation:
Department of Mathematics, University of Isfahan, PO Box 81746-73441, Isfahan, Iran School of Mathematics, Institute for Research in Fundamental Sciences (IPM), PO Box 19395-5746, Tehran, Iran (email: a_nasr_isfahani@yahoo.com)
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Abstract

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In this note we show that there exist a semiprime ring R, a strictly ordered artinian, narrow, unique product monoid (S,≤) and a monoid homomorphism ω:S⟶End(R) such that the skew generalized power series ring R[[S,ω]] is semicommutative but R[[S,ω]] is not reversible. This answers a question posed in Marks et al. [‘A unified approach to various generalizations of Armendariz rings’, Bull. Aust. Math. Soc.81 (2010), 361–397].

Keywords

skew generalized power series ringsemicommutativereversible

MSC classification

Secondary: 16S99: None of the above, but in this section 16U80: Generalizations of commutativity
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 84 , Issue 3 , December 2011 , pp. 455 - 457
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2011

References

[1]Marks, G., Mazurek, R. and Ziembowski, M., ‘A unified approach to various generalizations of Armendariz rings’, Bull. Aust. Math. Soc. 81 (2010), 361–397.CrossRefGoogle Scholar
[2]Mazurek, R. and Ziembowski, M., ‘On von Neumann regular rings of skew generalized power series’, Comm. Algebra 36(5) (2008), 1855–1868.CrossRefGoogle Scholar