SOME EXAMPLES OF ARMENDARIZ RINGS

Ayoub Elshokry; Eltiyeb Ali

Ayoub Elshokry Department of Mathematics, Faculty of Education, University of Khartoum,Omdurman, Sudan, P.O.Box 321, Sudan
Eltiyeb Ali Department of Mathematics, Faculty of Education, University of Khartoum, Omdurman, Sudan, P.O.Box 321, Sudan

Keywords: Monoid rings, M-Armendariz rings, linear M-Armendariz rings, unique product monoid rings, P P-ring, Baer ring.

Abstract

We construct various examples of Armendariz and related rings by reviewing and extending some results concerning the structure of monoid M. In particular, we give some examples of Armendariz rings related to a monoid. We prove that, if M be a strictly totally ordered monoid with |M| ≥ 2. Then, R is linear M-Armendariz and reduced if and only if T(R) is linear M-Armendariz. It is also shown that, R is a P P-ring (Baer ring) if and only if R[M] is a P P-ring (Baer ring, respectively) and those of the monoid ring R[M] in case R is linear M-Armendariz ring.

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