On nuclei of sup-$\Sigma$-algebras

Document Type: Research Paper

Authors

School of Mathematical Sciences‎, ‎South China Normal‎ ‎University‎, ‎510631 Guangzhou‎, ‎China.

Abstract

‎In this paper‎, ‎algebraic investigations on sup-$\Sigma$-algebras are presented‎. ‎A representation theorem for‎ ‎sup-$\Sigma$-algebras in terms of nuclei and quotients is obtained‎. ‎Consequently‎, ‎the relationship between‎ ‎the congruence lattice of a sup-$\Sigma$-algebra and the lattice of its nuclei is fully developed.

Keywords

Main Subjects


G. Birkhoff and J.D. Lipson, Heterogeneous algebra, J. Combin. Theory 8 (1970) 115--133.

D. Kruml and J. Paseka, Algebraic and categorical aspects of quantales, in: Handbook of Algebra, Vol. 5, pp. 323--362, Elsevier/North-Holland, Amsterdam, 2008.

J. Paseka, Projective sup-algebras: a general view, Topology Appl. 155 (2008) 308--317.

P. Resende, Tropological Systems and Observational Logic in Concurrency and Specification, PhD Thesis, IST, Universidade Técnica de Lisboa, 1998.

K. Rosenthal, Quantales and Their Applications, Longman Scientific & Technical, Essex, 1990.

C. Russo, Quantale Modules, Lambert Academic Publ. Saarbrucken, 2009.

S. Solovyov, A representation theorem for quantale algebras, in: Contributions to General Algebra 18, pp. 189--197, Heyn, Klagenfurt, 2008.

S. Solovyov, A note on nuclei of quantale algebras, Bull. Sect. Logic Univ.  Łódź40(2011) 91--112

D. Yetter, Quantales and non-commutative linear logic, J. Symb. Log. 55 (1990) 41--64.

X. Zhang and V. Laan, On injective hulls of S-posets. Semigroup Forum 91 (2015) 62--70.


Volume 43, Issue 6
November and December 2017
Pages 1709-1721
  • Receive Date: 20 May 2016
  • Revise Date: 21 September 2016
  • Accept Date: 06 October 2016