IJPAM: Volume 63, No. 1 (2010)

STRONGLY REVERSIBLE RINGS RELATIVE TO MONOID

Amit Bhooshan Singh$^1$, Prachi Juyal$^2$, M.R. Khan$^3$
$^{1,2,3}$Department of Mathematics
Faculty of Natural Sciences
Jamia Millia Islamia (Central University)
Delhi, 110025, INDIA
$^1$e-mail: [email protected]
$^2$e-mail: [email protected]
$^3$e-mail: [email protected]


Abstract.For a monoid $M$, we introduce strongly $M$-reversible rings, which are generalization of strongly reversible rings, and we investigate their properties. We show that if $G$ be a finitely generated Abelian group, then $G$ is torsionfree if and only if there exists a ring $R$ with $\vert R\vert\geq 2$ such that $R$ is strongly $M$-reversible. We also show that if $R$ is right or ring with right classical quotient ring $Q$, then $R$ is strongly $M$-reversible iff $Q$ is strongly $M$-reversible.

Received: March 7, 2010

AMS Subject Classification: 16N60, 16P60, 16U99, 16S15

Key Words and Phrases: unique product monoid, strongly reversible, strongly $M$-reversible

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2010
Volume: 63
Issue: 1