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partial algebras; varieties; weak subalgebras; weak equations
We study the weak hereditary class $S_{w}(\mathcal K)$ of all weak subalgebras of algebras in a total variety $\mathcal K$. We establish an algebraic characterization, in the sense of Birkhoff’s HSP theorem, and a syntactical characterization of these classes. We also consider the problem of when such a weak hereditary class is weak equational.
[1] H. Andréka, I.  Németi: Generalization of the concept of variety and quasivariety to partial algebras through category theory. Dissertationes Math. (Rozpr. Matem.) 204, (1983). MR 0709027
[2] P. Burmeister: A Model Theoretic Approach to Partial Algebras. Math. Research  32. Akademie-Verlag, Berlin, 1986. MR 0854861
[3] G. Grätzer, E. T.  Schmidt: Characterizations of congruence lattices of abstract algebras. Acta Sci. Math. (Szeged) 24 (1963), 34–59. MR 0151406
[4] D. Jakubíková-Studenovská: On completions of partial monounary algebras. Czechoslovak Math.  J. 38 (1988), 256–268. MR 0946294
[5] M.  Llabrés, F.  Rosselló: Pushout complements for arbitrary partial algebras. In: Proc. 6th International Workshop on Theory and Application of Graph Transformation TAGT’98. Lect. Notes in Comp. Sc.  1764, 2000, pp. 131–144. MR 1794795
[6] J.  Schmidt: A homomorphism theorem for partial algebras. Colloq. Math. 21 (1970), 5–21. MR 0281680 | Zbl 0199.32402
[7] B.  Staruch, B.  Staruch: Strong regular varieties of partial algebras. Alg. Univ. 31 (1994), 157–176. DOI 10.1007/BF01236515 | MR 1259347
[8] R. Szymański: Decidability of weak equational theories. Czechoslovak Math. J. 46 (1996), 629–664. MR 1414600
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