×

Residually small varieties of K-algebras. (English) Zbl 0482.08009


MSC:

08B10 Congruence modularity, congruence distributivity
16Rxx Rings with polynomial identity
Full Text: DOI

References:

[1] M. Chacron,On a theorem of Herstein, Canad. J. Math.21 (1969), 1348–1353. · Zbl 0213.04302 · doi:10.4153/CJM-1969-148-5
[2] –,On a theorem of Procesi, J. of Algebra15 (1970), 225–229. · Zbl 0222.16017 · doi:10.1016/0021-8693(70)90074-8
[3] B. Eckman andA. Schopf,Über injektiv Moduln, Arch, der Math.4 (1953), 75–78. · Zbl 0050.25904 · doi:10.1007/BF01899665
[4] R. Freese andR. McKenzie,Residually small varieties with modular congruence lattices, Trans. Amer. Math. Soc. 264 (1981), 419–430. · Zbl 0472.08008 · doi:10.1090/S0002-9947-1981-0603772-9
[5] R. Freeese andR. McKenzie,The commutator, an oveview, (preprint) 1981.
[6] J. Hagmann andC. Herrmann,A concrete ideal multiplication and its relation to congruence distributivity Arch. Math. (Basel)32, (1979), 234–245. · Zbl 0419.08001 · doi:10.1007/BF01238496
[7] I. N. Herstein,The structure of a certain class of rings, Amer. J. Math. 75 (1953) 886–871. · Zbl 0051.02501
[8] N. Jacobson,Structure of Rings, A.M.S. Colloq. Publ.37 (1964).
[9] –,The radical and semi-simplicity for arbitrary rings, Amer. J. Math.67 (1945), 300–320. · Zbl 0060.07305 · doi:10.2307/2371731
[10] –,Structure theory for algebraic algebras of bounded degree, Ann. of Math.46 (1945), 695–707. · Zbl 0060.07501 · doi:10.2307/1969205
[11] R. Kruse,Identities satisfied by a finite ring, J. of Algebra26 (1973), 298–318. · Zbl 0276.16014 · doi:10.1016/0021-8693(73)90025-2
[12] R. McKenzie,Residually small varieties of semigroups, Algebra Universalis (to appear). · Zbl 0475.20051
[13] C. Procesi,Rings with Polynomial Identities, Marcel Dekker Inc. (1973). · Zbl 0262.16018
[14] R. Quackenbush,Equational classes generated by finite algebras, Alg. Univ.1 (1971), 265–266. · Zbl 0231.08004 · doi:10.1007/BF02944989
[15] A. Rosenberg andD. Zelinsky,Finiteness of the injective hull, Math. Zeitschr.70 (1959) 372–380. · Zbl 0084.26505 · doi:10.1007/BF01558598
[16] J. D. H. Smith,Mal’cev Varieties, Lecture Notes in Math. 554, Springer-Verlag (1976). · Zbl 0344.08002
[17] W. Taylor,Residually small varieties, Alg. Univ.2 (1972), 33–53. · Zbl 0263.08005 · doi:10.1007/BF02945005
[18] W. Taylor, Equational logic, appendix to G. Grätzer,Universal Algebra, Springer-Verlag (1978).
[19] H. Werner andR. Wille,Charakterisierungen der primitiven Klassen arithmetischer Ringe, Math. Zeitschr.115 (1970), 197–200. · Zbl 0216.33701 · doi:10.1007/BF01109858
[20] A. P. Zamyatin,Varieties of associative rings whose elementary theory is decidable, Soviet Math. Doklady17 (1976), 996–999. · Zbl 0356.02041
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.