Inverse rings and inverse semigroups of ring homomorphisms

Adel Afif Abdelkarim


In this paper, a ring is an inverse ring if its multiplicative semigroup is an inverse semigroup. We show that an inverse ring contains no nilpotent elements except 0 and that it is a subring of a subdirect product of skew fields.

Let $R=Z_{n}$. Let $(H(R),\circ )$ be the semigroup of ring homomorphisms(under composition) on $R$. We show that $H(R)$ is a commutative inverse semigroup and it is of order $2^{n}$ and that each of its elements has order 2 or less.

We show that the set of regular-ring homomorphisms on $%Z_{p}[x]$, where $p$ is a prime, is an inverse semigroup.


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Published: 2012-10-12

How to Cite this Article:

Adel Afif Abdelkarim, Inverse rings and inverse semigroups of ring homomorphisms, Journal of Semigroup Theory and Applications, Vol 1 (2012), 46-52

Copyright © 2012 Adel Afif Abdelkarim. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Journal of Semigroup Theory and Applications

ISSN 2051-2937

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