{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T13:29:22Z","timestamp":1753882162001,"version":"3.41.2"},"reference-count":25,"publisher":"World Scientific Pub Co Pte Ltd","issue":"08","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2023,11]]},"abstract":"<jats:p> The notions of regular, intra regular and duo bi-acts of a Morita context of monoids have been introduced. Some characterizations of regular and intra regular bi-acts have been obtained in terms of b-subacts. Also connections among regularity of acts and [Formula: see text]-regularity of power semimodules, intra regularity of acts and intra [Formula: see text]-regularity of power semimodules have been observed using power functor. Then the study of the interplay among various components of a Morita context of monoids in terms of regularity, intra regularity and duoness have been accomplished. It has been deduced that regularity, intra regularity and being duo are Morita invariant properties. Finally regular (intra regular, duo) Morita context has been defined and it has been proved that for a duo Morita context of monoids regular and intra regular Morita context coincide. <\/jats:p>","DOI":"10.1142\/s1793830922501671","type":"journal-article","created":{"date-parts":[[2022,9,25]],"date-time":"2022-09-25T14:14:23Z","timestamp":1664115263000},"source":"Crossref","is-referenced-by-count":0,"title":["On regularity and intra regularity of the components of a Morita context of monoids"],"prefix":"10.1142","volume":"15","author":[{"given":"Kaushik","family":"Chakraborty","sequence":"first","affiliation":[{"name":"Department of Mathematics, Jadavpur University, Jadavpur, Kolkata 700032, India"}]},{"given":"Sujit Kumar","family":"Sardar","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Jadavpur University, Jadavpur, Kolkata 700032, India"}]},{"given":"K. P.","family":"Shum","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Yunan University, P. R. China"}]}],"member":"219","published-online":{"date-parts":[[2022,10,31]]},"reference":[{"key":"S1793830922501671BIB001","doi-asserted-by":"crossref","first-page":"257","DOI":"10.1007\/BF02572805","volume":"22","author":"Anjaneyulu A.","year":"1981","journal-title":"Semigroup Forum"},{"key":"S1793830922501671BIB002","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1007\/BF02996922","volume":"8","author":"Banaschewski B.","year":"1972","journal-title":"Abhandlungen aus dem Math. Seminar der Univ. Hamburg"},{"issue":"2","key":"S1793830922501671BIB003","doi-asserted-by":"crossref","first-page":"315","DOI":"10.2140\/pjm.1976.65.315","volume":"65","author":"Cheatham T. J.","year":"1976","journal-title":"Pacific J. Math."},{"key":"S1793830922501671BIB004","first-page":"45","volume":"67","author":"Chakraborty K.","year":"2021","journal-title":"An. Stiint. Univ. Al. I. Cuza Iasi. Mat. Tomul"},{"key":"S1793830922501671BIB005","volume-title":"The Algebraic Theory of Semigroups","volume":"1","author":"Clifford A. H.","year":"1961"},{"issue":"8","key":"S1793830922501671BIB006","doi-asserted-by":"crossref","first-page":"2409","DOI":"10.1080\/00927879708825998","volume":"25","author":"Dauns J.","year":"1997","journal-title":"Comm. Algebra"},{"key":"S1793830922501671BIB007","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511809088","volume-title":"Introduction to Lattice and Order","author":"Davey B. A.","year":"2002"},{"issue":"1","key":"S1793830922501671BIB008","doi-asserted-by":"crossref","first-page":"1950023","DOI":"10.1142\/S1793557119500232","volume":"12","author":"Dey K.","year":"2019","journal-title":"Asian Eur. J. Math."},{"key":"S1793830922501671BIB009","doi-asserted-by":"crossref","DOI":"10.1007\/978-94-015-9333-5","volume-title":"Semirings and Their Applications","author":"Golan J. S.","year":"1999"},{"key":"S1793830922501671BIB010","doi-asserted-by":"crossref","first-page":"163","DOI":"10.2307\/1969317","volume":"54","author":"Green J. A.","year":"1951","journal-title":"Ann. Math."},{"issue":"1","key":"S1793830922501671BIB011","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1007\/s00233-014-9682-0","volume":"92","author":"Gupta S.","year":"2016","journal-title":"Semigroup Forum"},{"issue":"1","key":"S1793830922501671BIB012","doi-asserted-by":"crossref","first-page":"1850014","DOI":"10.1142\/S1793557118500146","volume":"11","author":"Gupta S.","year":"2018","journal-title":"Asian-Eur. J. Math."},{"key":"S1793830922501671BIB013","doi-asserted-by":"publisher","DOI":"10.1142\/S0219498811004793"},{"key":"S1793830922501671BIB014","doi-asserted-by":"crossref","DOI":"10.1515\/9783110812909","volume-title":"Monoids, Acts and Categories","author":"Kilp M.","year":"2000"},{"key":"S1793830922501671BIB015","first-page":"359","author":"Knauer U.","year":"1972","journal-title":"Semigroup Forum"},{"issue":"8","key":"S1793830922501671BIB016","first-page":"710","volume":"45","author":"Lajos S.","year":"1969","journal-title":"Proc. Japan Acad."},{"issue":"9","key":"S1793830922501671BIB017","first-page":"626","volume":"39","author":"Lajos S.","year":"1963","journal-title":"Proc. Japan Acad."},{"key":"S1793830922501671BIB018","first-page":"85","volume":"6","author":"Morita K.","year":"1958","journal-title":"Science Rep. Tokyo Kyoiku Daigaku Sec. A"},{"key":"S1793830922501671BIB019","doi-asserted-by":"crossref","first-page":"707","DOI":"10.1073\/pnas.22.12.707","volume":"22","author":"Neumann J. V.","year":"1936","journal-title":"Proc. Nat. Acad. Sci."},{"issue":"2","key":"S1793830922501671BIB020","doi-asserted-by":"crossref","first-page":"1650023","DOI":"10.1142\/S0219498816500237","volume":"15","author":"Sardar S. K.","year":"2016","journal-title":"J. Algebra Appl."},{"issue":"1","key":"S1793830922501671BIB021","doi-asserted-by":"crossref","first-page":"985","DOI":"10.1142\/S1005386715000826","volume":"22","author":"Sardar S. K.","year":"2015","journal-title":"Algebra Colloq."},{"key":"S1793830922501671BIB022","first-page":"297","volume":"43","author":"Sardar S. K.","year":"2019","journal-title":"Southeast Asian Bull. Math."},{"issue":"3","key":"S1793830922501671BIB023","first-page":"371381","volume":"29","author":"Sardar S. K.","year":"2018","journal-title":"Afrika Mat."},{"key":"S1793830922501671BIB024","doi-asserted-by":"crossref","first-page":"273","DOI":"10.1007\/BF01848077","volume":"16","author":"Tran L. H.","year":"1985","journal-title":"Period. Math. Hung."},{"key":"S1793830922501671BIB025","doi-asserted-by":"crossref","first-page":"341","DOI":"10.1090\/S0002-9947-1972-0286843-3","volume":"163","author":"Zelmanowitz J.","year":"1972","journal-title":"Trans. Amer. Math. Soc."}],"container-title":["Discrete Mathematics, Algorithms and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1793830922501671","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,8,15]],"date-time":"2023-08-15T02:53:16Z","timestamp":1692067996000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/10.1142\/S1793830922501671"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,10,31]]},"references-count":25,"journal-issue":{"issue":"08","published-print":{"date-parts":[[2023,11]]}},"alternative-id":["10.1142\/S1793830922501671"],"URL":"https:\/\/doi.org\/10.1142\/s1793830922501671","relation":{},"ISSN":["1793-8309","1793-8317"],"issn-type":[{"type":"print","value":"1793-8309"},{"type":"electronic","value":"1793-8317"}],"subject":[],"published":{"date-parts":[[2022,10,31]]},"article-number":"2250167"}}