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Finitely Generated Modules Over Bezout Ringsrwiegand@Unl.Edu, Roger Wiegand, Sylvia Wiegand

Nebraska Cooperative Fish and Wildlife Research Unit: Staff Publications

Let R be a Bezout ring (a commutative ring in which all finitely generated ideals are principal), and let M be a finitely generated R -module. We will study questions of the following sort: (A) If every localization of M can be generated by n elements, can M itself be generated by n elements? (B) If M 0 R m = Rn for some m, n, is Af necessarily free? (C) If every localization of M has an element with zero annihilator, does M itself have such an element? We will answer these and related questions for various familiar classes …