On annihilator ideals of a polynomial ring over a noncommutative ring

By Y. Hirano. 2002

215 citations recorded by the source corpus.

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A taxonomy of 2-primal rings (2003, unknown): “Smoktunowicz; see [15,25,29], and [48].”
A GENERALIZATION OF PP-RINGS AND p.q.-BAER RINGS (2006, background): “Results and examples of quasi-Armendariz rings appeared in [11].”
A UNIFIED APPROACH TO VARIOUS GENERALIZATIONS OF ARMENDARIZ RINGS (2010, unknown): “As a consequence of Theorem 3.4, we obtain the following generalization of [12, Corollary 3.3], which was provided to counterpoint Kerr’s example of a polynomial ring over a Goldie ring that is not a Goldie ring.”
Semi-commutativity and the McCoy condition (2006, background): “(2) implies deg((f1 +f2)a2) deg(f1 +f2), which is impossible since f1 = f2.”
McCoy rings and zero-divisors (2008, methodology): “Hirano [3] proved that if R[x] is semi-commutative then R is McCoy, using an idea similar to one used by McCoy in [13].”
Power Series Rings Satisfying a Zero Divisor Property (2006, background): “Based on this result, nonreduced Armendariz rings were studied by Anderson and Camillo (1998), Hirano (2002), Huh et al. (2002), Kim and Lee (2000), Rege and Chhawchharia (1997), and so on.”
Rings with Property (A) and their extensions (2007, background): “But there exists a semicommutative ring which is not right McCoy [23, Claims 6 and 7].”
Armendariz and Reduced Rings (2004, background): “But, for an Armendariz ring R, R is Baer iff R½x is Baer (Armendariz, 1974; Kim and Lee, 2000), and R is right Goldie iff R½x is right Goldie (Hirano, 2002).”