Subdirectly irreducible algebras in regular permutable varieties
HTML articles powered by AMS MathViewer
- by W. Taylor PDF
- Proc. Amer. Math. Soc. 75 (1979), 196-200 Request permission
Abstract:
If A is a finite algebra in a regular, permutable variety (of finite type), then the variety generated by A either contains an infinite subdirectly irreducible algebra or contains only finitely many subdirectly irreducible algebras. We conjecture that the hypothesis “regular and permutable” cannot be fully removed.References
- John T. Baldwin, The number of subdirectly irreducible algebras in a variety. II, Algebra Universalis 11 (1980), no. 1, 1–6. MR 593008, DOI 10.1007/BF02483077
- John T. Baldwin and Joel Berman, The number of subdirectly irreducible algebras in a variety, Algebra Universalis 5 (1975), no. 3, 379–389. MR 392765, DOI 10.1007/BF02485271
- B. Csákány, Characterizations of regular varieties, Acta Sci. Math. (Szeged) 31 (1970), 187–189. MR 272697
- George Grätzer, Universal algebra, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto, Ont.-London, 1968. MR 0248066
- G. Grätzer, Two Mal′cev-type theorems in universal algebra, J. Combinatorial Theory 8 (1970), 334–342. MR 279022
- Hanna Neumann, Varieties of groups, Springer-Verlag New York, Inc., New York, 1967. MR 0215899
- Robert W. Quackenbush, Equational classes generated by finite algebras, Algebra Universalis 1 (1971/72), 265–266. MR 294222, DOI 10.1007/BF02944989
- Walter Taylor, Residually small varieties, Algebra Universalis 2 (1972), 33–53. MR 314726, DOI 10.1007/BF02945005 —, Residual finiteness in congruence-regular and permutable varieties, Notices Amer. Math. Soc. 25 (1978), A-350.
- Rudolf Wille, Kongruenzklassengeometrien, Lecture Notes in Mathematics, Vol. 113, Springer-Verlag, Berlin-New York, 1970 (German). MR 0262149
Additional Information
- © Copyright 1979 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 75 (1979), 196-200
- MSC: Primary 08B05
- DOI: https://doi.org/10.1090/S0002-9939-1979-0532134-4
- MathSciNet review: 532134