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Proceedings of the American Mathematical Society

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Representable monoids


Author: Earl J. Taft
Journal: Proc. Amer. Math. Soc. 70 (1978), 1-4
MSC: Primary 20M25; Secondary 20M30
DOI: https://doi.org/10.1090/S0002-9939-1978-0486253-0
MathSciNet review: 0486253
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Abstract: A representable monoid is one with enough representative functions to separate points. It is shown that the monoid algebra of a representable monoid is a proper algebra. In particular, the group algebra of a residually-finite group is a proper algebra. It is also shown that the free product of two representable monoids is again representable.


References [Enhancements On Off] (What's this?)

  • [H] G. Hochschild, Introduction to affine algebraic groups, Holden-Day, San Francisco, Calif., 1971. MR 0277535 (43:3268)
  • [ROB] D. J. S. Robinson, Finiteness conditions and generalized soluble groups, Part 1, Ergebnisse der Math., Band 62, Springer-Verlag, Berlin and New York, 1972. MR 0332989 (48:11314)
  • [ROS] A. Rosenberg, On the application of coalgebras to group algebras, Proc. Amer. Math. Soc. 52 (1975), 109-112. MR 0382331 (52:3216)
  • [S] M. Sweedler, Hopf algebras, Benjamin, New York, 1969. MR 0252485 (40:5705)
  • [T I] E. J. Taft, Reflexivity of algebras and coalgebras, Amer. J. Math. 94 (1972), 1111-1130. MR 0309992 (46:9095)
  • [T II] -, Reflexivity of algebras and coalgebras.II, Comm. Algebra 5 (1977), 1549-1560. MR 0480625 (58:781)
  • [W] B. A. F. Wehrfritz, Infinite linear groups, Ergebnisse der Math., Band 76, Springer-Verlag, Berlin and New York, 1973. MR 0335656 (49:436)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1978-0486253-0
Keywords: Representative function, representable monoid, monoid algebra, proper algebra, free product
Article copyright: © Copyright 1978 American Mathematical Society

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