{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,11]],"date-time":"2026-03-11T15:44:24Z","timestamp":1773243864058,"version":"3.50.1"},"reference-count":21,"publisher":"World Scientific Pub Co Pte Lt","issue":"01","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Algebra Appl."],"published-print":{"date-parts":[[2011,2]]},"abstract":"<jats:p> Any finite set of linear operators on an algebra A yields an operator algebra B and a module structure on A, whose endomorphism ring is isomorphic to a subring A<jats:sup>B<\/jats:sup> of certain invariant elements of A. We show that if A is a critically compressible left B-module, then the dimension of its self-injective hull \u00c2 over the ring of fractions of A<jats:sup>B<\/jats:sup> is bounded by the uniform dimension of A and the number of linear operators generating B. 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. <\/jats:p>","DOI":"10.1142\/s0219498811004446","type":"journal-article","created":{"date-parts":[[2011,3,24]],"date-time":"2011-03-24T01:21:22Z","timestamp":1300929682000},"page":"101-117","source":"Crossref","is-referenced-by-count":3,"title":["IRREDUCIBLE ACTIONS AND COMPRESSIBLE MODULES"],"prefix":"10.1142","volume":"10","author":[{"given":"IN\u00caS","family":"BORGES","sequence":"first","affiliation":[{"name":"Instituto Superior de Contabilidade e Administra\u00e7\u00e3o de Coimbra, Quinta Agr\u00edcola, Bencanta, 3040-316 Coimbra, Portugal"}]},{"given":"CHRISTIAN","family":"LOMP","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1tica da Faculdade de Ci\u00eancias da Universidade do Porto, Rua Campo Alegre 687, 4169-007 Porto, Portugal"}]}],"member":"219","published-online":{"date-parts":[[2012,4,30]]},"reference":[{"key":"rf1","volume":"171","author":"Albuquerque H.","journal-title":"J. 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