模的相对同余模拟簇
Relatively congruence modular quasivarieties of modules
摘要：
我们证明了左$R$ -模的相对同余模拟簇的拟方程理论是由$R$中的双边理想和左理想的滤子决定的.双边理想编码的单位元，保持在拟簇，而左理想的过滤器编码的拟单位元。左理想的滤子定义了挠的广义概念。从我们的结果可以得出：如果$R$是左Artinian环，则左$R$ -模的任何相对同余模拟簇都可由一组恒等式和至多一个真拟恒等式公理化;如果$R$是交换Artinian环，则左$R$ -模的任何相对同余模拟簇都是簇.
英文摘要：
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.
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