Skew Hurwitz Series Rings and Modules With Beachy-Bliar Conditions
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Authors: R. K. SHARMA AND A. B. SINGH
DOI: 10.46793/KgJMat2304.511S
Abstract:
A ring R satisfies the right Beachy-Blair condition if for every faithful right ideal J of a ring R (that is, a right ideal J of a ring R is faithful if rR(J) = 0) is co-faithful (that is, a right ideal J of a ring R is called co-faithful if there exists a finite subset J1 ⊆ J such that rR(J1) = 0). In this note, we prove two main results.
- Let R be a ring which is skew Hurwitz series-wise Armendariz, ω-compatible and torsion-free as a ℤ-module, and ω be an automorphism of R. If R satisfies the right Beachy-Blair condition then the skew Hurwitz series ring (HR,ω) satisfies the right Beachy-Blair condition.
- Let MR be a right R-module which is ω-Armendariz of skew Hurwitz series type and torsion-free as a ℤ-module, and ω be an automorphism of R. If MR satisfies the right Beachy-Blair condition then the skew Hurwitz series module HM(HR,ω) satisfies the right Beachy-Blair condition.
Keywords:
Ring with right Beachy-Blair condition, right R-module with right Beachy-Blair condition, skew Hurwitz series ring, skew Hurwitz series module, reduced ring, ω-compatible ring, ω-compatible module, ω-reduced module.
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