Characterizations of schunck classes of finite groups |
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Authors: | A Ballester-Bolinches LM Ezquerro |
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Institution: | 1. Departimento d'àlgebra , Universitat de Valèrcin. , C/ Dr. Moliner 50, Burjasot, Valercia, 46100, Spain;2. Departimento di Matemática e Informática , Universided Péblca de Nauarra Campus de Arrosadia , Pamplona, 31006, Spain |
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Abstract: | We prove a number of results concerning Armendariz rings and Gaussian rings. Recall that a (commutative) ring R is (Gaussian) Armendariz if for two polynomials f,g∈RX] (the ideal of R generated by the coefficients of f g is the product of the ideals generated by the coefficients of f and g) fg = 0 implies a i b j=0 for each coefficient a i of f and b j of g. A number of examples of Armendariz rings are given. We show that R Armendariz implies that RX] is Armendariz and that for R von Neumann regularR is Armendariz if and only if R is reduced. We show that R is Gaussian if and only if each homomorphic image of R is Armendariz. Characterizations of when RX] and RX] are Gaussian are given. |
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Keywords: | Armendariz ring Gaussian ring |
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