PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
2007 | 27 | 2 | 169-186
Tytuł artykułu

Pseudocomplements in sum-ordered partial semirings

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We study a particular way of introducing pseudocomplementation in ordered semigroups with zero, and characterise the class of those pseudocomplemented semigroups, termed g-semigroups here, that admit a Glivenko type theorem (the pseudocomplements form a Boolean algebra). Some further results are obtained for g-semirings - those sum-ordered partially additive semirings whose multiplicative part is a g-semigroup. In particular, we introduce the notion of a partial Stone semiring and show that several well-known elementary characteristics of Stone algebras have analogues for such semirings.
Twórcy
  • Department of Computer Science, University of Latvia, Riga LV-1586, Latvia
Bibliografia
  • [1] G. Birkhoff, Lattice Theory, AMS Colloq. Publ. 25, Providence, Rhode Island 1967.
  • [2] T.S. Blyth, Pseudo-residuals in semigroups, J. London Math. Soc. 40 (1965), 441-454.
  • [3] J. Cīrulis, Quantifiers in semiring like logics, Proc. Latvian Acad. Sci. 57 B (2003), 87-92.
  • [4] A. Dvurečenskij and S. Pulmannová, New Trends in Quantum Structures, Kluwer Acad. Publ. and Ister Science, Dordrecht, Bratislava e.a., 2000.
  • [5] O. Frink, Representation of Boolean algebras, Bull. Amer. Math. Soc. 47 (1941), 755-756.
  • [6] O. Frink, Pseudo-complements in semilattices, Duke Math. J. 29 (1962), 505-514.
  • [7] G. Grätzer, General Lattice Theory, Akademie-Verlag, Berlin, 1978.
  • [8] U. Hebisch and H.J. Weinert, Semirings. Algebraic Theory and Applications in Computer Science, World Scientific, Singapore e.a., 1993.
  • [9] J.M. Howie, Fundamentals of Semigroup Theory, Clarendon Press, Oxford 1995.
  • [10] M. Jackson and T. Stokes, Semilattice pseudo-complements on semigroups, Commun. Algebra 32 (2004), 2895-2918.
  • [11] M.F. Janowitz and C.S. Johnson, Jr., A note on Brouwerian and Glivenko semigroups, J. London Math. Soc. (2) 1 (1969), 733-736.
  • [12] E.G. Manes and D.B. Benson, The inverse semigroup of a sum-ordered semiring, Semigroup Forum 31 (1985), 129-152.
  • [13] T.P. Speed, A note on commutative semigroups, J. Austral. Math. Soc. 111 (1968), 731-736.
  • [14] U.M. Swamy and G.C. Rao e.a., Birkhoff centre of a poset, South Asia Bull. Math. 26 (2002), 509-516.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1125
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.