SOME EXAMPLES OF ARMENDARIZ RINGS

Ayoub Elshokry, Eltiyeb Ali

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.

Keywords


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

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References


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