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In the first part, we present relationships between ideals, weak ideals, congruences, and perfectness within MV-algebras and quasi MV-algebras, respectively. To achieve this goal, we provide a comprehensive characterization of congruence relations of a quasi MV-algebra\n \n \n $${\\mathcal {A}}$$<\/jats:tex-math>\n \n A<\/mml:mi>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n concerning the congruence relations of its MV-algebra of regular elements of\n \n \n $${\\mathcal {A}}$$<\/jats:tex-math>\n \n A<\/mml:mi>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n , along with specific equivalence relations concerning the complement of the set of regular elements. In the second part, we concentrate on perfect quasi MV-algebras. We present their representation by symmetric quasi\n \n \n $$\\ell $$<\/jats:tex-math>\n \n \u2113<\/mml:mi>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n -groups, a special kind of quasi\n \n \n $$\\ell $$<\/jats:tex-math>\n \n \u2113<\/mml:mi>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n -groups. Moreover, we establish a categorical equivalence of the category of perfect quasi MV-algebras, the category of\n n<\/jats:italic>\n -perfect quasi MV-algebras, and the category of symmetric quasi\n \n \n $$\\ell $$<\/jats:tex-math>\n \n \u2113<\/mml:mi>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n -groups.\n <\/jats:p>","DOI":"10.1007\/s11225-024-10156-8","type":"journal-article","created":{"date-parts":[[2025,2,25]],"date-time":"2025-02-25T15:17:52Z","timestamp":1740496672000},"page":"65-101","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Some Results on Quasi MV-Algebras and Perfect Quasi MV-Algebras"],"prefix":"10.1007","volume":"114","author":[{"given":"Anatolij","family":"Dvure\u010denskij","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2178-9421","authenticated-orcid":false,"given":"Omid","family":"Zahiri","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2025,2,25]]},"reference":[{"key":"10156_CR1","doi-asserted-by":"publisher","first-page":"387","DOI":"10.1007\/s11083-008-9103-7","volume":"25","author":"LP Belluce","year":"2008","unstructured":"Belluce, L.P., A. Di Nola, and B. Gerla, Abelian $$\\ell $$-groups with strong unit and perfect MV-algebras, Order 25: 387\u2013401, 2008. https:\/\/doi.org\/10.1007\/s11083-008-9103-7","journal-title":"Order"},{"key":"10156_CR2","doi-asserted-by":"publisher","unstructured":"Bou, F., F. Paoli, A. Ledda, and H. Freytes, On some properties of $$\\sqrt{^{\\prime }}$$ quasi-MV algebras and quasi-MV algebras. Part II, Soft Computing 12(4): 341\u2013352, 2008. https:\/\/doi.org\/10.1007\/s00500-007-0185-8","DOI":"10.1007\/s00500-007-0185-8"},{"issue":"2","key":"10156_CR3","doi-asserted-by":"publisher","first-page":"619","DOI":"10.1093\/logcom\/exp080","volume":"20","author":"F Bou","year":"2010","unstructured":"Bou, F., F. Paoli, A. Ledda, M. Spinks, and R. Giuntini, The logic of quasi-MV algebras, The Journal of Logic and Computation 20(2): 619\u2013643, 2010. https:\/\/doi.org\/10.1093\/logcom\/exp080","journal-title":"The Journal of Logic and Computation"},{"key":"10156_CR4","doi-asserted-by":"publisher","first-page":"467","DOI":"10.2307\/1993227","volume":"88","author":"CC Chang","year":"1958","unstructured":"Chang, C.C., Algebraic analysis of many-valued logics, Transactions of the American Mathematical Society 88: 467\u2013490, 1958. https:\/\/doi.org\/10.2307\/1993227","journal-title":"Transactions of the American Mathematical Society"},{"issue":"1","key":"10156_CR5","doi-asserted-by":"publisher","first-page":"19","DOI":"10.1515\/ms-2015-0112","volume":"66","author":"W Chen","year":"2016","unstructured":"Chen, W., and W.A. Dudek, Quantum computational algebra with a non-commutative generalization, Mathematica Slovaca 66(1): 19\u201334, 2016. https:\/\/doi.org\/10.1515\/ms-2015-0112","journal-title":"Mathematica Slovaca"},{"key":"10156_CR6","doi-asserted-by":"publisher","first-page":"3879","DOI":"10.1007\/s00500-017-2854-6","volume":"22","author":"W Chen","year":"2018","unstructured":"Chen, W., and W.A. Dudek, Ideals and congruences in quasi-pseudo-MV algebras, Soft Computing 22: 3879\u20133889, 2018. https:\/\/doi.org\/10.1007\/s00500-017-2854-6","journal-title":"Soft Computing"},{"issue":"5","key":"10156_CR7","doi-asserted-by":"publisher","first-page":"655","DOI":"10.1093\/jigpal\/jzw034","volume":"24","author":"W Chen","year":"2016","unstructured":"Chen, W., and B. Davvaz, Some classes of quasi-pseudo-MV algebras, Logic Journal of the IGPL 24(5): 655\u2013672, 2016. https:\/\/doi.org\/10.1093\/jigpal\/jzw034","journal-title":"Logic Journal of the IGPL"},{"key":"10156_CR8","doi-asserted-by":"publisher","unstructured":"Cignoli, R., I. M. L. D\u2019Ottaviano and D. Mundici, Algebraic Foundations of Many-Valued Reasoning, Springer Science and Business Media, Dordrecht, 2000. https:\/\/doi.org\/10.1007\/978-94-015-9480-6","DOI":"10.1007\/978-94-015-9480-6"},{"key":"10156_CR9","volume-title":"Theory of Lattice-Ordered Groups","author":"M Darnel","year":"1994","unstructured":"Darnel, M. Theory of Lattice-Ordered Groups, CRC Press, USA, 1994."},{"key":"10156_CR10","doi-asserted-by":"publisher","unstructured":"Di Nola, A., and A. 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