{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T00:39:16Z","timestamp":1759970356895,"version":"build-2065373602"},"reference-count":21,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2025,1,23]],"date-time":"2025-01-23T00:00:00Z","timestamp":1737590400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Science Fund of the Republic of Serbia","award":["6565"],"award-info":[{"award-number":["6565"]}]},{"name":"Advanced Techniques of Mathematical Aggregation and Approximative Equations Solving in Digital Operational Research","award":["6565"],"award-info":[{"award-number":["6565"]}]},{"name":"AT-MATADOR","award":["6565"],"award-info":[{"award-number":["6565"]}]},{"name":"Ministry of Science, Technological Development and Innovation of the Republic of Serbia","award":["6565"],"award-info":[{"award-number":["6565"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>Following the notions of \u03a9-set and \u03a9-algebra where \u03a9 is a complete lattice, we introduce P-algebras, replacing the lattice \u03a9 by a poset P. A P-algebra is a classical algebraic structure in which the usual equality is replaced by a P-valued equivalence relation, i.e., with the symmetric and transitive map from the underlying set into a poset P. In addition, this generalized equality is (as a map) compatible with the fundamental operations of the algebra. The diagonal restriction of this map is a P-valued support of a P-algebra. The particular subsets of this support, its cuts, are classical subalgebras, while the cuts of the P-valued equality are congruences on the corresponding cut subalgebras. We prove that the collection of the corresponding quotients of these cuts is a centralized system in the lattice of weak congruences of the basic algebra. We also describe the canonical representation of P-algebras, independent of the poset P.<\/jats:p>","DOI":"10.3390\/axioms14020081","type":"journal-article","created":{"date-parts":[[2025,1,23]],"date-time":"2025-01-23T05:49:54Z","timestamp":1737611394000},"page":"81","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["P-Algebras"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8117-4413","authenticated-orcid":false,"given":"Elijah Eghosa","family":"Edeghagba","sequence":"first","affiliation":[{"name":"Mathematical Institute SANU, 11000 Belgrade, Serbia"},{"name":"Department of Mathematics, Bauchi State University, Gadau 751105, Nigeria"}]},{"given":"Branimir","family":"\u0160e\u0161elja","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Informatics, Faculty of Sciences, University of Novi Sad, 21000 Novi Sad, Serbia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5716-604X","authenticated-orcid":false,"given":"Andreja","family":"Tepav\u010devi\u0107","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Bauchi State University, Gadau 751105, Nigeria"},{"name":"Department of Mathematics and Informatics, Faculty of Sciences, University of Novi Sad, 21000 Novi Sad, Serbia"}]}],"member":"1968","published-online":{"date-parts":[[2025,1,23]]},"reference":[{"key":"ref_1","unstructured":"Klir, G.J., and Yuan, B. 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