{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,15]],"date-time":"2024-09-15T22:27:51Z","timestamp":1726439271982},"reference-count":40,"publisher":"World Scientific Pub Co Pte Ltd","issue":"05","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2003,10]]},"abstract":"<jats:p>A semiring with involution is a semiring equipped with an involutorial antiasutomorphism as a fundamental operation. The aim of the present paper is to determine the lattice of all varieties of idempotent and distributive semirings with involution. We start with the description of their structure, which is followed by a complete list of all subdirectly irreducibles. We make a heavy use of general results obtained recently by Dolinka and Vin\u010di\u0107 [11] on involutorial P\u0142onka sums. Applying these results and some further structural theorems, we construct the considered lattice. It turns out that it has exactly 64 elements.<\/jats:p>","DOI":"10.1142\/s0218196703001614","type":"journal-article","created":{"date-parts":[[2004,1,13]],"date-time":"2004-01-13T04:14:02Z","timestamp":1073967242000},"page":"597-625","source":"Crossref","is-referenced-by-count":2,"title":["IDEMPOTENT DISTRIBUTIVE SEMIRINGS WITH INVOLUTION"],"prefix":"10.1142","volume":"13","author":[{"given":"IGOR","family":"DOLINKA","sequence":"first","affiliation":[{"name":"Department of Mathematics and Informatics, University of Novi Sad, Trg Dositeja Obradovi\u0107a 4, 21000 Novi Sad, Serbia and Montenegro"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1016\/0021-8693(82)90042-4"},{"key":"rf2","first-page":"255","volume":"9","author":"Biryukov A. P.","journal-title":"Algebra i Logika"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1007\/BF01190768"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-3975(99)00079-1"},{"key":"rf5","first-page":"423","volume":"36","author":"Crvenkovi\u0107 S.","journal-title":"Studia Sci. Math. Hung."},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1080\/00927870008826995"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1007\/s002330010025"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1023\/A:1010379324510"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1007\/s000120050176"},{"key":"rf10","first-page":"535","volume":"67","author":"Dolinka I.","journal-title":"Acta Sci. Math. (Szeged)"},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1023\/A:1025797422998"},{"key":"rf12","first-page":"337","volume":"29","author":"Dudek J.","journal-title":"Bull. Acad. Pol. Sci. (Ser. Sci. Math.)"},{"key":"rf13","doi-asserted-by":"publisher","DOI":"10.1016\/0304-3975(94)00041-G"},{"key":"rf15","first-page":"648","volume":"11","author":"Foulis D. J.","journal-title":"Proc. Amer. Math. Soc."},{"key":"rf16","doi-asserted-by":"publisher","DOI":"10.1016\/0021-8693(70)90073-6"},{"volume-title":"The Theory of Semirings with Applications in Mathematics and Theoretical Computer Science","year":"1993","author":"Golan J. S.","key":"rf17"},{"key":"rf18","series-title":"The structure of finite algebras","volume-title":"Contemporary Mathematics Series","volume":"76","author":"Hobby D.","year":"1988"},{"key":"rf19","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198511946.001.0001","volume-title":"Fundamentals of Semigroup Theory","author":"Howie J. M.","year":"1995"},{"key":"rf20","unstructured":"B.\u00a0J\u00f3nsson, Algebraic Logic, The theory of binary relations\u00a054 (North-Holland, Amsterdam, 1991)\u00a0pp. 245\u2013292."},{"key":"rf21","doi-asserted-by":"crossref","first-page":"161","DOI":"10.4064\/fm-71-2-161-163","volume":"71","author":"Kalman J. A.","journal-title":"Fund. Math."},{"key":"rf22","series-title":"Semirings, automata and languages","volume-title":"EATCS Monographs on Theoretical Computer Science","author":"Kuich W.","year":"1986"},{"key":"rf24","doi-asserted-by":"publisher","DOI":"10.1215\/S0012-7094-72-03954-3"},{"key":"rf25","doi-asserted-by":"crossref","unstructured":"R.\u00a0McKenzie, Algebra and Logic, An algebraic version of categorical equivalence for varieties and more general algebraic categories\u00a0180 (Marcel Dekker, New York, 1996)\u00a0pp. 211\u2013243.","DOI":"10.1201\/9780203748671-10"},{"key":"rf26","volume-title":"Algebras, Lattices, Varieties","volume":"1","author":"McKenzie R.","year":"1987"},{"key":"rf27","unstructured":"R.\u00a0McKenzie and A.\u00a0Romanowska, Contributions to General Algebra, Varieties of \u00b7-distributive bisemilattices (J. Heyn, Klagenfurt, 1979)\u00a0pp. 213\u2013218."},{"key":"rf28","doi-asserted-by":"publisher","DOI":"10.1007\/BF02194636"},{"key":"rf29","doi-asserted-by":"publisher","DOI":"10.1007\/BF02572828"},{"key":"rf30","doi-asserted-by":"publisher","DOI":"10.1007\/BF02884266"},{"key":"rf31","first-page":"239","volume":"44","author":"Pastijn F.","journal-title":"Acta Sci. Math. (Szeged)"},{"key":"rf32","first-page":"77","volume":"36","author":"Pastijn F.","journal-title":"Arch. Math. (Brno)"},{"key":"rf33","doi-asserted-by":"crossref","first-page":"191","DOI":"10.4064\/fm-60-2-191-200","volume":"60","author":"P\u0142onka J.","journal-title":"Fund. Math."},{"key":"rf34","doi-asserted-by":"crossref","first-page":"183","DOI":"10.4064\/fm-61-2-183-189","volume":"61","author":"P\u0142onka J.","journal-title":"Fund. Math."},{"key":"rf35","doi-asserted-by":"crossref","first-page":"241","DOI":"10.4064\/fm-64-2-241-247","volume":"64","author":"P\u0142onka J.","journal-title":"Fund. Math."},{"key":"rf36","unstructured":"J.\u00a0P\u0142onka and A.\u00a0Romanowska, Universal Algebra and Quasigroup Theory, Semilattice sums (Heldermann Verlag, Berlin, 1992)\u00a0pp. 123\u2013158."},{"key":"rf37","first-page":"467","volume":"27","author":"Romanowska A.","journal-title":"Math. Japonica"},{"key":"rf38","first-page":"483","volume":"27","author":"Romanowska A.","journal-title":"Math. Japonica"},{"key":"rf39","doi-asserted-by":"publisher","DOI":"10.1016\/0021-8693(81)90244-1"},{"key":"rf40","doi-asserted-by":"publisher","DOI":"10.1016\/0021-8693(89)90197-X"},{"key":"rf41","doi-asserted-by":"publisher","DOI":"10.1016\/0021-8693(89)90198-1"},{"key":"rf42","first-page":"25","volume":"70","author":"Wagner V. V.","journal-title":"U\u010d. Zap. Saratov. Univ. Meh.-Mat."}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218196703001614","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,1,11]],"date-time":"2024-01-11T17:03:13Z","timestamp":1704992593000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218196703001614"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2003,10]]},"references-count":40,"journal-issue":{"issue":"05","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2003,10]]}},"alternative-id":["10.1142\/S0218196703001614"],"URL":"https:\/\/doi.org\/10.1142\/s0218196703001614","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"type":"print","value":"0218-1967"},{"type":"electronic","value":"1793-6500"}],"subject":[],"published":{"date-parts":[[2003,10]]}}}