Koubek, V.; Sichler, J. Universal varieties of distributive double p-algebras. (English) Zbl 0574.06009 Glasg. Math. J. 26, 121-131 (1985). A category C is called (a) universal, if any full category of algebras is isomorphic to a full subcategory of C. (b) iso-universal, if, for any full category of algebras A, Iso(A) is isomorphic to a full subcategory of Iso(C). Answering a question of E. Fried, the authors exhibit a finitely generated universal variety of distributive double p-algebras. They also show that the following are equivalent for any finitely generated variety V of distributive double p-algebras: (i) V is not congruence permutable, (ii) V contains a subdirectly irreducible algebra which is not simple, (iii) The variety of double Stone algebras is contained in V, (iv) V is iso-universal. Reviewer: I.Düntsch Cited in 8 Documents MSC: 06D15 Pseudocomplemented lattices 08C05 Categories of algebras 08B99 Varieties 06B20 Varieties of lattices Keywords:full category of algebras; finitely generated universal variety of distributive double p-algebras; subdirectly irreducible algebra; double Stone algebras PDFBibTeX XMLCite \textit{V. Koubek} and \textit{J. Sichler}, Glasg. Math. J. 26, 121--131 (1985; Zbl 0574.06009) Full Text: DOI References: [1] DOI: 10.1007/BF02485824 · Zbl 0353.06002 · doi:10.1007/BF02485824 [2] DOI: 10.1007/BF02485372 · Zbl 0381.06019 · doi:10.1007/BF02485372 [3] DOI: 10.1007/BF02945029 · Zbl 0256.06004 · doi:10.1007/BF02945029 [4] Pultr, Combinatorial, Algebraic and Topological Representations of Groups, Semigroups and Categories (1980) [5] DOI: 10.1093/qmath/26.1.215 · Zbl 0323.06013 · doi:10.1093/qmath/26.1.215 [6] DOI: 10.1112/plms/s3-24.3.507 · Zbl 0323.06011 · doi:10.1112/plms/s3-24.3.507 [7] DOI: 10.1112/blms/2.2.186 · Zbl 0201.01802 · doi:10.1112/blms/2.2.186 [8] Nachbin, Topology and Order (1965) [9] DOI: 10.1007/BF02485733 · Zbl 0302.06022 · doi:10.1007/BF02485733 [10] Hedrlín, Illinois J. Math. 10 pp 392– (1966) [11] Jónsson, Math. Scand. 21 pp 110– (1967) · Zbl 0167.28401 · doi:10.7146/math.scand.a-10850 [12] Hedrlin, Canad. J. Math. 18 pp 1237– (1966) · Zbl 0145.20603 · doi:10.4153/CJM-1966-121-7 [13] DOI: 10.1007/BF02944963 · Zbl 0236.18003 · doi:10.1007/BF02944963 [14] Davey, Ordered Sets 83 pp 43– (1982) · doi:10.1007/978-94-009-7798-3_2 [15] Adams, Glasgow Math. J. 20 pp 81– (1979) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.