Categories of universal algebras in which direct products are tensor products
Abstract
In categories of commutative universal algebras of given types we discover full subcategories in which direct products coincide with tensor products.
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2. B. Banaschewski, E. Nelson, Tensor products and bimorphisms, Canad. Math. Bull. 19 (1976), 385-402.
3. A.H. Clifford, G.B. Preston, The Algebraic Theory of Semigroups, Providence, Rhode Island, 1964.
4. S. Eilenberg, G.M. Kelly, Closed categories, Proc. Conf. Cat. Alg. La Jolla, 1965, 421-562.
5. G. Grätzer, Universal Algebra, Second Ed., Springer Verlag, New York-Heidelberg-Berlin, 1979.
6. J. Ježek, T. Kepka, Medial groupoids, Rozpravy ČSAV, Řada Mat. a Přir. Věd. 93/1, Academia, Prague, 1983.
7. L. Klukovits, On commutative universal algebras, Acta. Sci. Math. 34 (1973), 171-174.
8. F.E. Linton, Autonomous equational categories, J. Math. Mech. 15 (1966), 637-642.
9. J. Płonka, Diagonal algebras, Fund. Math. 58 (1966), 309-321.
10. J. Šlapal, A note on diagonal algebras, Math. Nachr. 158 (1992), 195-197.
ŠlapalJ. (1995). Categories of universal algebras in which direct products are tensor products. Annales Mathematicae Silesianae, 9, 7-10. Retrieved from https://journals.us.edu.pl/index.php/AMSIL/article/view/14199
Josef Šlapal
Department of Mathematics, Technical University of Brno, Czech Republic Czechia
Department of Mathematics, Technical University of Brno, Czech Republic Czechia
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