Σ-genomorphism of algebraic structures

• Autorzy: Emanovský, P.
• Języki publikacji: EN

Abstrakty

EN

For an algebraic structure A = (A, F, R) of type τ and a set Σ of open formulas of the first order language L(τ), the concept of Σ-closed subset of A was introduced in [3]. The set C Σ(A) of all Σ-closed subsets of A forms a complete lattice whose properties were studied in [3], [4] and [5]. Algebraic structures A, B of type τ are called CΣ-isomorphic (or Σ-isomorphic in [3]) if the lattices CΣ(A) and CΣ(B) are isomorphic. The CΣ-isomorphisms are investigated for so-called Σ-separable algebraic structures in [3]. The study of the Σ-isomorphisms of algebraic structures is continued in this paper. We introduce the concepts of Σ-genomorphism and Σ-isogenomorphism of algebraic structures and we formulate a sufficient condition under which two structures are isomorphic. We show that for Σ-separable structures the condition is also necessary. Further, we introduce the concepts of Σ-morphism, congruential E -morphism and congruence induced by a congruential Σ-morphism. We also prove Theorem on Σ-genomorphism and Theorem on Σ-morphism.

Słowa kluczowe

PL

struktury algebraiczne; systemy zamknięte

EN

algebraic structure; closure system; genomorphism; congruence

• Czasopismo: Demonstratio Mathematica
• Rocznik: 2003
• Tom: Vol. 36, nr 4
• Strony: 785--792
• Opis fizyczny: Bibliogr. 10 poz.

Twórcy

autor

Emanovský, P.

• Department of Mathematics, Palacký University Olomouc, Žižkovo nám. 5, 771 40 Olomouc, Czech Republic,

Bibliografia

• [1] E. K. Blum, D. R. Estes, A generalization of the homomorphism concepts, Algebra Universalis 7 1977), 143-161.
• [2] I. Chajda, Lattice in quasiordered sets, Acta Univ. Palack. Olom. 31 (1992), 6-12.
• [3] I. Chajda, P. Emanovský, Σ-isomorphic algebraic structures, Math. Bohem. 120 (1995), 71-81.
• [4] I. Chajda, P. Emanovský, Modularity and distributivity of the lattice of Σ-closed subsets of an algebraic structure, Math. Bohem. 120 (1995), 209-217.
• [5] I. Chajda, P. Emanovský, Σ-hamiltonian and Σ-regular algebraic structures, Math. Bohem. 121 (1996), 177-182.
• [6] P. Emanovský, Convex isomorphic ordered sets, Math. Bohem. 118 (1993), 29-35.
• [7] P. Emanovský, Convex isomorphism of q-lattices, Math. Bohem. 118 (1993), 37-42.
• [8] G. Grätzer, Universal Algebra (2nd edition), Springer Verlag, 1979.
• [9] A. I. Malcev, Algebraic Systems (Russian), Nauka, Moskva, 1970.
• [10] V. I. Marmazejev, The lattice of convex sublattices of a lattice (Russian), Mezvužovskij naučnyj sbornik 6 (1986), Saratov, 50-58.