Relatively Congruence Modular Quasivarieties of Modules
نویسنده
چکیده
We show that the quasiequational theory of a relatively congruence modular quasivariety of left R-modules is determined by a two-sided ideal in R together with a filter of left ideals. The two-sided ideal encodes the identities that hold in the quasivariety, while the filter of left ideals encodes the quasiidentities. The filter of left ideals defines a generalized notion of torsion. It follows from our result that if R is left Artinian, then any relatively congruence modular quasivariety of left R-modules is axiomatizable by a set of identities together with at most one proper quasiidentity, and if R is a commutative Artinian ring then any relatively congruence modular quasivariety of left R-modules is a variety. Dedicated to Don Pigozzi
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