{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,11]],"date-time":"2026-03-11T15:40:16Z","timestamp":1773243616867,"version":"3.50.1"},"reference-count":22,"publisher":"Cambridge University Press (CUP)","issue":"A","license":[{"start":{"date-parts":[[2010,6,24]],"date-time":"2010-06-24T00:00:00Z","timestamp":1277337600000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Glasgow Math. J."],"published-print":{"date-parts":[[2010,7]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>The purpose of this paper is to study finiteness conditions on injective hulls of simple modules over Noetherian down-up algebras. We will show that the Noetherian down-up algebras <jats:italic>A<\/jats:italic>(\u03b1, \u03b2, \u03b3) which are fully bounded are precisely those which are module-finite over a central subalgebra. We show that injective hulls of simple <jats:italic>A<\/jats:italic>(\u03b1, \u03b2, \u03b3)-modules are locally Artinian provided the roots of <jats:italic>X<\/jats:italic><jats:sup>2<\/jats:sup> \u2212 \u03b1<jats:italic>X<\/jats:italic> \u2212 \u03b2 are distinct roots of unity or both equal to 1.<\/jats:p>","DOI":"10.1017\/s0017089510000261","type":"journal-article","created":{"date-parts":[[2010,6,24]],"date-time":"2010-06-24T06:18:44Z","timestamp":1277360324000},"page":"53-59","source":"Crossref","is-referenced-by-count":12,"title":["INJECTIVE MODULES OVER DOWN-UP ALGEBRAS"],"prefix":"10.1017","volume":"52","author":[{"given":"PAULA A. A. 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