Non-singular covers over ordered monoid rings
Copyright policy )Non-singular covers over ordered monoid rings
Summary: Let \(G\) be a multiplicative monoid. If \(RG\) is a non-singular ring such that the class of all non-singular \(RG\)-modules is a cover class, then the class of all non-singular \(R\)-modules is a cover class. These two conditions are equivalent whenever \(G\) is a well-ordered cancellative monoid such that for all elements \(g,h\in G\) with \(g
non-singular rings, cover classes, Goldie torsion theory, non-singular modules, Torsion theories, radicals, semigroup rings, Other classes of modules and ideals in associative algebras, torsion theories of finite type, precover classes, Ordinary and skew polynomial rings and semigroup rings, hereditary torsion theories, Injective modules, self-injective associative rings, Ordered semigroups and monoids, Torsion theories; radicals on module categories (associative algebraic aspects)
non-singular rings, cover classes, Goldie torsion theory, non-singular modules, Torsion theories, radicals, semigroup rings, Other classes of modules and ideals in associative algebras, torsion theories of finite type, precover classes, Ordinary and skew polynomial rings and semigroup rings, hereditary torsion theories, Injective modules, self-injective associative rings, Ordered semigroups and monoids, Torsion theories; radicals on module categories (associative algebraic aspects)
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