Linear Armendriz Ring Relative to Monoid
نویسندگان
چکیده
For a monoid M , we introduce linear M-Armendariz rings, which are generalization of M-Armendariz rings and linear Armendariz rings; and investigate their properties. Every reduced ring is linear M-Armendariz, for any unique product monoid. We show that if M be a monoid and R be a right ore ring with classical right quotient ring Q. Then R is linear M-Armendariz if and only if Q is linear M-Armendariz. We also show that let G be a finitely generated Abelian group. Then G is torsion-free iff there exists a ring with |R| ≥ 2 such that R is linear G-Armendariz. Mathematics Subject Classification: 16N60, 16S36, 16P60, 16U20
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