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Annihilating content in polynomial and power series rings. (English) Zbl 1427.13024

Let \(R\) be a commutative ring with unity. The authors define \(R\) to be an EM-ring (probably as the initials of their own first names Emad and Manal) if each polynomial \(f(X)\in R[X]\) can be written as \(f(X)=c_ff_1(X)\) with \(c_f\in R\) and \(f_1(X)\) is not a zero-divisor of \(R[X]\). They show that the class of EM-rings includes integral domains, principal ideal rings, Bézout rings, Baer rings, von Neumann rings and PP-rings, while it is included in Armendariz rings and rings having a.c. condition. Some analogous rings are defined for power series and the tow notions are compared.

MSC:

13F20 Polynomial rings and ideals; rings of integer-valued polynomials
13F25 Formal power series rings
13E05 Commutative Noetherian rings and modules
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