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2003 | 23 | 2 | 101-114
Tytuł artykułu

On lattice-ordered monoids

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In the paper lattice-ordered monoids and specially normal lattice-ordered monoids which are a generalization of dually residuated lattice-ordered semigroups are investigated. Normal lattice-ordered monoids are metricless normal lattice-ordered autometrized algebras. It is proved that in any lattice-ordered monoid A, a ∈ A and na ≥ 0 for some positive integer n imply a ≥ 0. A necessary and sufficient condition is found for a lattice-ordered monoid A, such that the set I of all invertible elements of A is a convex subset of A and A¯ ⊆ I, to be the direct product of the lattice-ordered group I and a lattice-ordered semigroup P with the least element 0.
Rocznik
Tom
23
Numer
2
Strony
101-114
Opis fizyczny
Daty
wydano
2003
otrzymano
2002-11-26
otrzymano
2003-05-16
otrzymano
2003-12-20
Twórcy
autor
  • Department of Mathematics, Faculty of Chemical Technology, Slovak Technical University, Radlinského 9, 812 37 Bratislava, Slovak Republic
Bibliografia
  • [1] G. Birkhoff, Lattice Theory, Third edition, Amer. Math. Soc., Providence, RI, 1967.
  • [2] A.C. Choudhury, The doubly distributive m-lattice, Bull. Calcutta. Math. Soc. 47 (1957), 71-74.
  • [3] L. Fuchs, Partially ordered algebraic systems, Pergamon Press, New York 1963.
  • [4] M. Hansen, Minimal prime ideals in autometrized algebras, Czech. Math. J. 44 (119) (1994), 81-90.
  • [5] M. Jasem, Weak isometries and direct decompositions of dually residuated lattice-ordered semigroups, Math. Slovaca 43 (1993), 119-136.
  • [6] T. Kovár, Any DRl-semigroup is the direct product of a commutative l-group and a DRl-semigroup with the least element, Discuss. Math.-Algebra & Stochastic Methods 16 (1996), 99-105.
  • [7] T. Kovár, A general theory of dually residuated lattice-ordered monoids, Ph.D. Thesis, Palacký Univ., Olomouc 1996.
  • [8] T. Kovár, Two remarks on dually residuated lattice-ordered semigroups, Math. Slovaca 49 (1999), 17-18.
  • [9] T. Kovár, On (weak) zero-fixing isometries in dually residuated lattice-ordered semigroups, Math. Slovaca 50 (2000), 123-125.
  • [10] T. Kovár, Normal autometrized lattice-ordered algebras, Math. Slovaca, 50 (2000), 369-376.
  • [11] J. Rachnek, Prime ideals in autometrized algebras, Czechoslovak Math. J. 37 (112) (1987), 65-69.
  • [12] J. Rachnek, Polars in autometrized algebras, Czechoslovak Math. J. 39 (114) (1989), 681-685.
  • [13] J. Rachnek, Regular ideals in autometrized algebras, Math. Slovaca 40 (1990), 117-122.
  • [14] J. Rachnek, DRl-semigroups and MV-algebras, Czechoslovak Math. J. 48 (123) (1998), 365-372.
  • [15] J. Rachnek, MV-algebras are categorically equivalent to a class of DRl1(i)-semigroups, Math. Bohemica 123 (1998), 437-441.
  • [16] K.L.N. Swamy, Dually residuated lattice-ordered semigroups, Math. Ann. 159 (1965), 105-114.
  • [17] K.L.N. Swamy, Dually residuated lattice-ordered semigroups. II, Math. Ann. 160 (1965), 64-71.
  • [18] K.L.N. Swamy, Dually residuated lattice-ordered semigroups. III, Math. Ann. 167 (1966), 71-74.
  • [19] K.L.N. Swamy and N.P. Rao, Ideals in autometrized algebras, J. Austral. Math. Soc. Ser. A 24 (1977), 362-374.
  • [20] K.L.N. Swamy and B.V. Subba Rao, Isometries in dually residuated lattice-ordered semigroups, Math. Sem. Notes Kobe Univ. 8 (1980), 369-379.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1066
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