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2012 | 32 | 1 | 5-21
Tytuł artykułu

On ideals of a skew lattice

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Ideals are one of the main topics of interest when it comes to the study of the order structure of an algebra. Due to their nice properties, ideals have an important role both in lattice theory and semigroup theory. Two natural concepts of ideal can be derived, respectively, from the two concepts of order that arise in the context of skew lattices. The correspondence between the ideals of a skew lattice, derived from the preorder, and the ideals of its respective lattice image is clear. Though, skew ideals, derived from the partial order, seem to be closer to the specific nature of skew lattices. In this paper we review ideals in skew lattices and discuss the intersection of this with the study of the coset structure of a skew lattice.
Rocznik
Tom
32
Numer
1
Strony
5-21
Opis fizyczny
Daty
wydano
2012
otrzymano
2011-10-05
poprawiono
2012-06-25
Twórcy
  • University of Ljubljana
Bibliografia
  • [1] A. Bauer and K. Cvetko-Vah, Stone duality for skew Boolean algebras with intersections, Arxiv preprint arXiv:1106.0425, Houston Journal of Mathematics (to appear, 2012).
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  • [5] K. Cvetko-Vah and J. Pita Costa, On the coset laws for skew lattices, Semigroup Forum 8 (2011) 395-411. doi: 10.1007/s00233-011-9325-7
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  • [15] J. Leech, Recent developments in the theory of skew lattices, Semigroup Forum 52 (1996) 7-24. doi: 10.1007/BF02574077
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  • [17] J. Pita Costa, Coset Laws for Categorical Skew Lattices (Algebra Univers., in press, 2011).
  • [18] J. Pita Costa, On the coset structure of skew lattices, Demonstratio Mathematica 44 (4) (2011) 1-19.
  • [19] J. Pita Costa, On the Coset Structure of Skew Lattices (PhD thesis, University of Ljubljana, 2012).
  • [20] B.M. Schein, Pseudosemilattices and pseudolattices, Amer. Math. Soc. Transl. 119 (1983) 1-16.
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  • [22] W. Wechler, Universal Algebra for Computer Scientists (Springer-Verlag, Berlin, 1992). doi: 10.1007/978-3-642-76771-5
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_7151_dmal_1187
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