{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,26]],"date-time":"2026-05-26T01:02:10Z","timestamp":1779757330160,"version":"3.53.1"},"reference-count":30,"publisher":"Oxford University Press (OUP)","issue":"3","license":[{"start":{"date-parts":[[2026,5,12]],"date-time":"2026-05-12T00:00:00Z","timestamp":1778544000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12331016"],"award-info":[{"award-number":["12331016"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2026,5,26]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>In this paper, we introduce the variety of equality algebras endowed with universal quantifiers (called uE-algebras), and establish an equivalent category for the corresponding category. Most significantly, we present an expansion of uE-algebras by enriching them with an internal state operator (which are referred to as state uE-algebras), and investigate some of their fundamental algebraic properties. In particular, we discuss the correspondence between state m-deductive systems and m-congruences of state uE-algebras. We also provide a set of characterizations for subdirectly irreducible state uE-algebras, together with characterizations for local and simple state-morphism uE-algebras, which play a crucial role in studying the variety of state uE-algebras. Finally, using the notion of adjoint m-pairs, we obtain a representation for state-morphism operators on uE-algebras.<\/jats:p>","DOI":"10.1093\/jigpal\/jzag026","type":"journal-article","created":{"date-parts":[[2026,4,17]],"date-time":"2026-04-17T12:50:47Z","timestamp":1776430247000},"source":"Crossref","is-referenced-by-count":0,"title":["A state operator on the uE-algebra"],"prefix":"10.1093","volume":"34","author":[{"given":"Ya","family":"Wei","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics , Shaanxi Normal University, Xi\u2019an, 710119, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Bin","family":"Zhao","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics , Shaanxi Normal University, Xi\u2019an, 710119, 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