{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,6,22]],"date-time":"2022-06-22T09:15:35Z","timestamp":1655889335282},"reference-count":20,"publisher":"World Scientific Pub Co Pte Ltd","issue":"05","funder":[{"name":"the Shota Rustaveli National Science Foundation of Georgia","award":["FR-18-10849"],"award-info":[{"award-number":["FR-18-10849"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2022,8]]},"abstract":"<jats:p> We define the product of admissible abstract kernels of the form [Formula: see text], where [Formula: see text] is a monoid, [Formula: see text] is a group and [Formula: see text] is a monoid homomorphism. Identifying [Formula: see text]-equivalent abstract kernels, where [Formula: see text] is the center of [Formula: see text], we obtain that the set [Formula: see text] of [Formula: see text]-equivalence classes of admissible abstract kernels inducing the same action of [Formula: see text] on [Formula: see text] is a commutative monoid. Considering the submonoid [Formula: see text] of abstract kernels that are induced by special Schreier extensions, we prove that the factor monoid [Formula: see text] is an abelian group. Moreover, we show that this abelian group is isomorphic to the third cohomology group [Formula: see text]. <\/jats:p>","DOI":"10.1142\/s0218196722500436","type":"journal-article","created":{"date-parts":[[2022,5,9]],"date-time":"2022-05-09T12:58:41Z","timestamp":1652101121000},"page":"1009-1041","source":"Crossref","is-referenced-by-count":0,"title":["The third cohomology group of a monoid and admissible abstract kernels"],"prefix":"10.1142","volume":"32","author":[{"given":"Nelson","family":"Martins-Ferreira","sequence":"first","affiliation":[{"name":"ESTG, CDRSP, Instituto Polit\u00e9cnico de Leiria, Leiria, Portugal"}]},{"given":"Andrea","family":"Montoli","sequence":"additional","affiliation":[{"name":"Dipartimento di Matematica \u201cFederigo Enriques\u201d, Universit\u00e0 degli Studi di Milano, Via Saldini 50, 20133 Milano, Italy"}]},{"given":"Alex","family":"Patchkoria","sequence":"additional","affiliation":[{"name":"A. Razmadze Mathematical Institute, Ivane Javakhishvili Tbilisi State University, Tamarashvili Str. 6, Tbilisi 0177, Georgia"}]},{"given":"Manuela","family":"Sobral","sequence":"additional","affiliation":[{"name":"CMUC and Departamento de Matem\u00e1tica, Universidade de Coimbra, 3001-501 Coimbra, Portugal"}]}],"member":"219","published-online":{"date-parts":[[2022,5,6]]},"reference":[{"key":"S0218196722500436BIB001","first-page":"451","volume":"24","author":"Bourn D.","year":"2010","journal-title":"Theory Appl. Categ."},{"key":"S0218196722500436BIB002","series-title":"Textos de Matem\u00e1tica (S\u00e9rie B)","volume-title":"Schreier Split Epimorphisms in Monoids and in Semirings","volume":"45","author":"Bourn D.","year":"2013"},{"key":"S0218196722500436BIB003","doi-asserted-by":"publisher","DOI":"10.1016\/j.jpaa.2012.02.015"},{"key":"S0218196722500436BIB004","doi-asserted-by":"publisher","DOI":"10.1023\/B:APCS.0000013810.93405.c8"},{"key":"S0218196722500436BIB005","doi-asserted-by":"publisher","DOI":"10.1016\/j.jalgebra.2016.03.015"},{"key":"S0218196722500436BIB006","doi-asserted-by":"publisher","DOI":"10.1016\/j.jalgebra.2013.03.020"},{"key":"S0218196722500436BIB007","doi-asserted-by":"publisher","DOI":"10.2307\/1969174"},{"key":"S0218196722500436BIB008","doi-asserted-by":"publisher","DOI":"10.4310\/HHA.2001.v3.n1.a6"},{"key":"S0218196722500436BIB009","doi-asserted-by":"publisher","DOI":"10.1215\/S0012-7094-47-01473-7"},{"key":"S0218196722500436BIB010","doi-asserted-by":"publisher","DOI":"10.2307\/2372712"},{"key":"S0218196722500436BIB011","first-page":"316","volume":"2","author":"Lane S. Mac","year":"1958","journal-title":"Illinois J. Math."},{"key":"S0218196722500436BIB012","doi-asserted-by":"publisher","DOI":"10.1515\/forum-2019-0164"},{"key":"S0218196722500436BIB013","doi-asserted-by":"publisher","DOI":"10.1007\/s00233-016-9780-2"},{"key":"S0218196722500436BIB014","doi-asserted-by":"publisher","DOI":"10.1007\/s00233-018-9962-1"},{"key":"S0218196722500436BIB016","doi-asserted-by":"publisher","DOI":"10.1016\/0022-4049(72)90008-4"},{"key":"S0218196722500436BIB017","first-page":"21","volume":"86","author":"Patchkoria A.","year":"1977","journal-title":"Bull. Georgian Acad. Sci."},{"key":"S0218196722500436BIB019","first-page":"252","volume":"14","author":"R\u00e9dei L.","year":"1952","journal-title":"Acta Sci. Math. (Szeged)"},{"key":"S0218196722500436BIB020","doi-asserted-by":"publisher","DOI":"10.1007\/BF01694897"},{"key":"S0218196722500436BIB021","first-page":"276","volume":"4","author":"Schreier O.","year":"1926","journal-title":"Abh. Math. Semin. Univ. Hambg."},{"key":"S0218196722500436BIB022","first-page":"37","volume":"84","author":"Tuyen N. X.","year":"1976","journal-title":"Bull. Georgian Acad. Sci."}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218196722500436","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,6,22]],"date-time":"2022-06-22T08:35:12Z","timestamp":1655886912000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/10.1142\/S0218196722500436"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,5,6]]},"references-count":20,"journal-issue":{"issue":"05","published-print":{"date-parts":[[2022,8]]}},"alternative-id":["10.1142\/S0218196722500436"],"URL":"https:\/\/doi.org\/10.1142\/s0218196722500436","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"value":"0218-1967","type":"print"},{"value":"1793-6500","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,5,6]]}}}