5 research outputs found

    Irreducible actions and compressible modules

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    Any finite set of linear operators on an algebra AA yields an operator algebra BB and a module structure on A, whose endomorphism ring is isomorphic to a subring ABA^B of certain invariant elements of AA. We show that if AA is a critically compressible left BB-module, then the dimension of its self-injective hull AA over the ring of fractions of ABA^B is bounded by the uniform dimension of AA and the number of linear operators generating BB. This extends a known result on irreducible Hopf actions and applies in particular to weak Hopf action. Furthermore we prove necessary and sufficient conditions for an algebra A to be critically compressible in the case of group actions, group gradings and Lie actions

    Associative rings

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