The general structure of inverse polynomial modules. (English) Zbl 0983.16006

Summary: We compute injective, projective and flat dimensions of inverse polynomial modules as \(R[x]\)-modules. We also generalize Hom and Ext functors of inverse polynomial modules to any submonoid, but we show that Tor functor of inverse polynomial modules can be generalized only for a symmetric submonoid.


16E30 Homological functors on modules (Tor, Ext, etc.) in associative algebras
16E10 Homological dimension in associative algebras
16D50 Injective modules, self-injective associative rings
16S36 Ordinary and skew polynomial rings and semigroup rings
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