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After establishing the foundational structure theory for such quasi-L-algebras, we delve into the class of quasi-L-algebras, denoted as <jats:inline-formula>\n              <jats:alternatives>\n                <jats:tex-math>$$\\mathcal{Q}\\mathcal{L}$$<\/jats:tex-math>\n                <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mi>Q<\/mml:mi>\n                    <mml:mi>L<\/mml:mi>\n                  <\/mml:mrow>\n                <\/mml:math>\n              <\/jats:alternatives>\n            <\/jats:inline-formula>, which forms a quasivariety. Utilizing the fact that every quasi-L-algebra can be embedded into the direct product of an L-algebra and a flat quasi-L-algebra, we determine a generator for <jats:inline-formula>\n              <jats:alternatives>\n                <jats:tex-math>$$\\mathcal{Q}\\mathcal{L}$$<\/jats:tex-math>\n                <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mi>Q<\/mml:mi>\n                    <mml:mi>L<\/mml:mi>\n                  <\/mml:mrow>\n                <\/mml:math>\n              <\/jats:alternatives>\n            <\/jats:inline-formula>. Lastly, we explore congruence relations on a quasi-L-algebra <jats:italic>L<\/jats:italic> and their connections with ideals and weak ideals of <jats:italic>L<\/jats:italic>, as well as the ideals of the L-algebra <jats:italic>R<\/jats:italic>(<jats:italic>L<\/jats:italic>). We also propose a representation for congruence relations on each quasi-L-algebras.<\/jats:p>","DOI":"10.1007\/s00500-025-10567-2","type":"journal-article","created":{"date-parts":[[2025,5,5]],"date-time":"2025-05-05T09:36:57Z","timestamp":1746437817000},"page":"3125-3137","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Quasi-L-algebras"],"prefix":"10.1007","volume":"29","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2178-9421","authenticated-orcid":false,"given":"Omid","family":"Zahiri","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiao Long","family":"Xin","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2025,5,5]]},"reference":[{"issue":"1","key":"10567_CR1","first-page":"27","volume":"4","author":"M Aaly Kologani","year":"2023","unstructured":"Aaly Kologani M (2023) Relations between L-algebras and other logical algebras. 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