Leech, Jonathan Normal skew lattices. (English) Zbl 0754.06004 Semigroup Forum 44, No. 1, 1-8 (1992). This paper is divided into three sections. First, the authors give some basic facts and skew lattice analogues of some basic results of Yamada and Kimura. In the second section they focus attention on the principal theme, the connection between normality and distributivity. As main result they give a canonical factorization of a normal symmetric skew lattice into the fibered product of a lattice with a distributive skew lattice. The distributive case is considered in the final section, which contains analogues of several fundamental results about distributive lattices. Reviewer: R.Firlová (Havířov-Bludovice) Cited in 30 Documents MSC: 06B05 Structure theory of lattices 06D05 Structure and representation theory of distributive lattices Keywords:skew lattice; normality; distributivity; canonical factorization; fibered product PDF BibTeX XML Cite \textit{J. Leech}, Semigroup Forum 44, No. 1, 1--8 (1992; Zbl 0754.06004) Full Text: DOI EuDML References: [1] Gerhardts, M. D.,Zur Characterisierung distributiver Schiefverbande, Math. Ann.161 (1965), 231–240. · Zbl 0151.01701 · doi:10.1007/BF01361972 [2] Gratzer, G., ”Lattice Theory, First Concepts and Distributive Lattices,” W. H. Freeman and Co., San Francisco, 1971. [3] Howie, J., ”An Introduction to Semigroup Theory,” Academic Press, London, 1976. · Zbl 0355.20056 [4] Kimura, N.,The Structure of Idempotent Semigroups I, Pacific J. Math.8 (1958), 257–275. · Zbl 0084.02702 [5] Leech, J.,Skew Lattices in Rings, A. Universalis26 (1989), 48–72. · Zbl 0669.06006 · doi:10.1007/BF01243872 [6] Leech, J.,Skew Boolean Algebras, A. Universalis27 (1990), 497–506. · Zbl 0719.06010 · doi:10.1007/BF01188995 [7] Leech, J.,The Geometric Structure of Skew Lattices, Trans. Amer. Math. Soc., to appear. · Zbl 0792.06008 [8] Petrich, M., ”Lectures on Semigroups,” John Wiley and Sons, New York, 1977. · Zbl 0369.20036 [9] Schein, B. M.,On the Theory of Restrictive Semigroups, Izv. Vyss. Ucebn. Zav. Mat.33 (1963) (2), 152–154 (Russian). [10] Schein, B. M.,Pseudosemilattices and Pseudolattices, Amer. Math. Soc. Transl. (2)119 (1983), 1–16. [11] Schweigert, D.,Distributive Associative Near Lattices, Math. Slovaca35 (1985), 313–317. · Zbl 0578.06005 [12] Vagner, V. V.,Restrictive Semigroups, Izv. Vyss. Ucebn. Zav. Mat.31 (1962) (6), 19–27 (Russian). [13] Yamada, M. and N. Kimura,Note on Idempotent Semigroups II, Proc. Japan Acad.34 (1958), 110–112. · Zbl 0081.25501 · doi:10.3792/pja/1195524790 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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.