Results 141 to 150 of about 187 (161)
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ARMENDARIZ RINGS RELATIVE TO A MONOID
Communications in Algebra, 2005ABSTRACT For a monoid M, we introduce M-Armendariz rings, which are generalizations of Armendariz rings; and we investigate their properties. Every reduced ring is M-Armendariz for any unique product monoid M. We show that if R is a reduced and M-Armendariz ring, then R is M × N-Armendariz, where N is a unique product monoid.
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McCoy Rings Relative to a Monoid
Communications in Algebra, 2010For a monoid M, we introduce M-McCoy rings, which are a generalization of McCoy rings and M-Armendariz rings; and investigate their properties. We first show that all reversible rings are right M-McCoy, where M is a u.p.-monoid. We also show that all right duo rings are right M-McCoy, where M is a strictly totally ordered monoid.
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Monoid rings and related topics
1998Let ϕ be an injective endomorphism of a ring A. We denote by Al[[x, ϕ] the left skew (power) series ring consisting of formal series \( \sum\nolimits_{1 = 0}^\infty {a_i x^i }\) of the variable x with canonical coefficients ai ∈ A,where addition is defined naturally and multiplication is defined by the rule xi a = ϕ i(a)xi.
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A characterization of weakly Krull monoid algebras
Journal of Algebra, 2022Daniel Windisch, VÍCTOR Fadinger
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The monoid of regular elements in commutative rings with zero divisors
Communications in Algebra, 2022Gyu Whan Chang
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Monoid rings which are valuation rings
Communications in Algebra, 1983Jack Ohm, Paul Vicxnair
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General w-ZPI-Rings and a Tool for Characterizing Certain Classes of Monoid Rings
Communications in Algebra, 2023Jason Juett
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Unique factorization properties in commutative monoid rings with zero divisors
Semigroup Forum, 2021Christopher Park Mooney
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Monoidal Transforms of Regular Local Rings
American Journal of Mathematics, 1973openaire +2 more sources