{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,4]],"date-time":"2022-04-04T18:05:50Z","timestamp":1649095550650},"reference-count":4,"publisher":"World Scientific Pub Co Pte Lt","issue":"08","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2010,12]]},"abstract":"<jats:p> \u03b1-Irreducible and \u03b1-Strongly Irreducible Ideals of a ring have been characterized in [2] and [4]. A complete lattice which is generated by compact elements is called an algebraic lattice for the simple reason that every such lattice is isomorphic to the lattice of subalgebras of a suitable universal algebra and vice-versa. In this paper, we characterize the irreducible elements and strongly irreducible elements in an algebraic lattice, which extends the results in [4] to arbitrary algebraic lattices. Also we obtain certain necessary and sufficient conditions, in terms of irreducible elements, for an algebraic lattice to satisfy the complete distributivity. <\/jats:p>","DOI":"10.1142\/s0218196710005984","type":"journal-article","created":{"date-parts":[[2010,12,28]],"date-time":"2010-12-28T10:27:42Z","timestamp":1293532062000},"page":"969-975","source":"Crossref","is-referenced-by-count":1,"title":["IRREDUCIBLE ELEMENTS IN ALGEBRAIC LATTICES"],"prefix":"10.1142","volume":"20","author":[{"given":"U. M.","family":"SWAMY","sequence":"first","affiliation":[{"name":"Department of Mathematics, GVP College of Engineering, Madhurawada, Visakhapatnam, India"}]},{"given":"B.","family":"VENKATESWARLU","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Andhra University, Visakhapatnam\u2013530 003, India"}]}],"member":"219","published-online":{"date-parts":[[2012,4,30]]},"reference":[{"key":"rf1","series-title":"AMS Colloquium Publications","volume-title":"Lattice Theory","author":"Birkhoff G.","year":"1967"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1016\/S0022-4049(01)00043-3"},{"key":"rf3","volume-title":"A Course in Universal Algebra","author":"Stanely B.","year":"1980"},{"key":"rf4","first-page":"299","volume":"32","author":"Lu X.","journal-title":"Southeast Asian Bulletin of Mathematics"}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218196710005984","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T03:31:51Z","timestamp":1565148711000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218196710005984"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,12]]},"references-count":4,"journal-issue":{"issue":"08","published-online":{"date-parts":[[2012,4,30]]},"published-print":{"date-parts":[[2010,12]]}},"alternative-id":["10.1142\/S0218196710005984"],"URL":"https:\/\/doi.org\/10.1142\/s0218196710005984","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"value":"0218-1967","type":"print"},{"value":"1793-6500","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,12]]}}}