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Proceedings of the Estonian Academy of Sciences

ISSN 1736-7530 (electronic)   ISSN 1736-6046 (print)
Formerly: Proceedings of the Estonian Academy of Sciences, series Physics & Mathematics and  Chemistry
Published since 1952

Proceedings of the Estonian Academy of Sciences

ISSN 1736-7530 (electronic)   ISSN 1736-6046 (print)
Formerly: Proceedings of the Estonian Academy of Sciences, series Physics & Mathematics and  Chemistry
Published since 1952
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Quotients and subalgebras of sup-algebras; pp. 311–322

(Full article in PDF format) doi: 10.3176/proc.2015.3.16


Authors

Xia Zhang, Valdis Laan

Abstract

An ordered algebra is called a sup-algebra if its underlying poset is a complete lattice and its operations are compatible with joins in each variable. In this article we study quotients and subalgebras of sup-algebras. We show that the congruence lattice of a sup-algebra is isomorphic to the lattice of its nuclei and dually isomorphic to the lattice of its meet-closed subalgebras. We also prove that the lattice of subalgebras of a sup-algebra is isomorphic to the lattice of its conuclei.

Keywords

sup-algebra, nucleus, conucleus, congruence, quotient, subalgebra.

References

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  2. Czédli , G. and Lenkehegyi , A. On classes of ordered algebras and quasiorder distributivity. Acta Sci. Math. , 1983 , 46 , 41–54.

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  4. Kruml , D. and Paseka , J. Algebraic and categorical aspects of quantales. In Handbook of Algebra , Vol. 5 (Hazewinkel , M. , ed.). Elsevier , 2008 , 323–362.
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  7. Rosenthal , K. I. Quantales and Their Applications. Pitman Research Notes in Mathematics 234. Harlow , Essex , 1990.

  8. Russo , C. Quantale Modules. Lambert Academic Publishing , Saarbrücken , 2009.

  9. Solovyov , S. A representation theorem for quantale algebras. Contr. Gen. Alg. , 2008 , 18 , 189–198.

10. Solovyov , S. A note on nuclei of quantale algebras. Bull. Sect. Logic Univ. Lodz , 2011 , 40 , 91–112.

11. Zhang , X. and Laan , V. On injective hulls of S-posets. Semigroup Forum , 2015 , 91 , 62–70.
http://dx.doi.org/10.1007/s00233-014-9646-4

 
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Current Issue: Vol. 67, Issue 4 in Press, 2018




Publishing schedule:
No. 1: 20 March
No. 2: 20 June
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