{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,17]],"date-time":"2025-10-17T20:07:28Z","timestamp":1760731648011,"version":"build-2065373602"},"reference-count":26,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2025,3,6]],"date-time":"2025-03-06T00:00:00Z","timestamp":1741219200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Deanship of Scientific Research, Vice Presidency for Graduate Studies and Scientific Research, King Faisal University, Saudi Arabia","award":["KFU250321"],"award-info":[{"award-number":["KFU250321"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>A semigroup S is termed a generalized Clifford semigroup (GC-semigroup) if it forms a strong semilattice of \u03c0-groups. This paper explores necessary and sufficient conditions for a GC-monoid to be nearly complete within certain subclasses. These subclasses are distinguished by the nature of their linking homomorphisms, which may be bijective, surjective, injective, or image trivial. The findings provide a deeper understanding of the structural integrity and completeness of GC-monoids, contributing valuable insights to the theoretical framework of semigroup theory. Applications of this study span various fields, including cryptography for secure algorithm design, coding theory and quantum computing for advanced quantum algorithms. The established criteria also support further research in mathematical biology and automorphic theory, demonstrating the broad relevance and utility of nearly complete GC-monoids.<\/jats:p>","DOI":"10.3390\/sym17030398","type":"journal-article","created":{"date-parts":[[2025,3,6]],"date-time":"2025-03-06T06:02:13Z","timestamp":1741240933000},"page":"398","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Nearly Complete Generalized Clifford Monoids and Applications"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0009-0001-7770-8168","authenticated-orcid":false,"given":"Dilawar J.","family":"Mir","sequence":"first","affiliation":[{"name":"Department of Mathematics, CDOE, Chandigarh University, Mohali 140413, Punjab, India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6279-4959","authenticated-orcid":false,"given":"Bana","family":"Al Subaiei","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, College of Science, King Faisal University, P.O. Box 400, Al-Ahsa 31982, Saudi Arabia"}]},{"given":"Aftab H.","family":"Shah","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Central University of Kashmir, Ganderbal 191201, Jammu and Kashmir, India"}]}],"member":"1968","published-online":{"date-parts":[[2025,3,6]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Clifford, A.H., and Preston, G.B. (1961). Mathematical Surveys and Monographs. The Algebraic Theory of Semigroups, American Mathematical Society.","DOI":"10.1090\/surv\/007.1"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1060","DOI":"10.15672\/hujms.1244782","article-title":"Inner Automorphisms of Clifford Monoids","volume":"53","author":"Shah","year":"2024","journal-title":"Hacet. J. Math. Stat."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"2250002","DOI":"10.1142\/S281100722250002X","article-title":"On Automorphisms of Strong Semilattices of Groups","volume":"1","author":"Shah","year":"2022","journal-title":"Math. Open"},{"key":"ref_4","first-page":"3031","article-title":"On Automorphisms of Strong Semilattices of \u03c0-Groups","volume":"13","author":"Shah","year":"2022","journal-title":"Int. J. Nonlinear Anal. Appl."},{"key":"ref_5","unstructured":"Birkhoff, G. (1967). Lattice Theory, American Mathematical Society."},{"key":"ref_6","unstructured":"Herstein, I.N. (1975). Topics in Algebra, Wiley."},{"key":"ref_7","unstructured":"Grillet, P.A. (1995). Semigroups: An Introduction to the Structure Theory, CRC Pres."},{"key":"ref_8","first-page":"1341","article-title":"Automorphism Groups of Finite Semigroups","volume":"10","author":"Cain","year":"2011","journal-title":"J. Algebra Appl."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"261","DOI":"10.4064\/fm-28-1-261-264","article-title":"Uber Abbildungen einer absrakten Menge Auf ihre Telimengen","volume":"28","author":"Schreier","year":"1936","journal-title":"Fund Math."},{"key":"ref_10","first-page":"146","article-title":"Symmetric Groupoids","volume":"31","year":"1952","journal-title":"Math. Sbornik N. S."},{"key":"ref_11","first-page":"177","article-title":"Homomorphisms of the semigroups of all partial transformations","volume":"3","author":"Sutov","year":"1961","journal-title":"Izv. Vyss Ucebn Zaved Mat."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"73","DOI":"10.4153\/CMB-1966-009-7","article-title":"Automorphisms of semigroup of all relations on a set","volume":"9","author":"Magill","year":"1966","journal-title":"Can. Math. Bull."},{"key":"ref_13","first-page":"531","article-title":"On symmetric generalised groups","volume":"33","author":"Liber","year":"1953","journal-title":"Math. Sbornik N. S."},{"key":"ref_14","first-page":"105","article-title":"Semigroups and rings of endomorphisms of linear spaces-I","volume":"45","author":"Gluskin","year":"1965","journal-title":"Am. Math. Soc. Trans."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"413","DOI":"10.1017\/S1446788700034455","article-title":"Some results concerning a transformation semigroups","volume":"19","author":"Symons","year":"1975","journal-title":"J. Aust. Math. Soc."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1017\/S144678870002396X","article-title":"Automorphisms of Transformation semigroups","volume":"20","author":"Sullivan","year":"1975","journal-title":"J. Aust. Math. Soc."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"185","DOI":"10.1017\/S001309150002263X","article-title":"Automorphisms of normal Transformation semigroups","volume":"2","author":"Levi","year":"1985","journal-title":"Proc. Edinburg Math. Soc."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"2250032","DOI":"10.1142\/S1793557122500322","article-title":"On Automorphisms of Monotone Transformation posemigroups","volume":"15","author":"Mir","year":"2022","journal-title":"Asian-Eur. J. Math."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"20230161","DOI":"10.1515\/math-2023-0161","article-title":"On pomonoid of partial transformations of a poset","volume":"21","year":"2023","journal-title":"Open Math."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Mir, D.J., and Alali, A.S. (2024). On Centralizers of Idempotents with Restricted Range. Symmetry, 16.","DOI":"10.3390\/sym16060769"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1017\/S1446788709000019","article-title":"General Theorems on automorphisms of semigroups and their applications","volume":"87","author":"Konieczny","year":"2009","journal-title":"J. Aust. Math. Soc."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"373","DOI":"10.1016\/j.jsc.2009.10.001","article-title":"Computing automorphisms of semigroups","volume":"45","author":"Mitchell","year":"2010","journal-title":"J. Symb. Comput."},{"key":"ref_23","unstructured":"Petrich, M., and Reilly, N.R. (1999). Completely Regular Semigroups, Wiley."},{"key":"ref_24","unstructured":"Howie, J.M. (1995). Fundamentals of Semigroup Theory, Oxford University Press. Volume 12 of London Mathematical Society Monographs, New Series."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1078","DOI":"10.1080\/00029890.1966.11970898","article-title":"Mappings of Semigroups Associated with Ordered Pairs","volume":"73","author":"Vitanza","year":"1966","journal-title":"Am. Math. Mon."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"589","DOI":"10.29020\/nybg.ejpam.v11i3.3274","article-title":"The Srong Semilattices of \u03c0-Groups","volume":"3","author":"Zhang","year":"2018","journal-title":"Eur. J. Pure Appl. Math."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/3\/398\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T16:48:13Z","timestamp":1760028493000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/3\/398"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,3,6]]},"references-count":26,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2025,3]]}},"alternative-id":["sym17030398"],"URL":"https:\/\/doi.org\/10.3390\/sym17030398","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2025,3,6]]}}}