Cohomological dimension of an abelian monoid
HTML articles powered by AMS MathViewer
- by Charles Ching-an Cheng and Jay Shapiro PDF
- Proc. Amer. Math. Soc. 80 (1980), 547-551 Request permission
Abstract:
It is shown that the cohomological dimension of an abelian monoid is equal to that of its group reflection provided that the monoid is either finitely generated or cancellative.References
- S. Balcerzyk, The global dimension of the group rings of abelian groups. III, Fund. Math. 67 (1970), 241–250. MR 276369, DOI 10.4064/fm-67-2-241-250
- Henri Cartan and Samuel Eilenberg, Homological algebra, Princeton University Press, Princeton, N. J., 1956. MR 0077480
- A. H. Clifford and G. B. Preston, The algebraic theory of semigroups. Vol. I, Mathematical Surveys, No. 7, American Mathematical Society, Providence, R.I., 1961. MR 0132791
- G. L. Fel′dman, The homological dimension of group algebras of solvable groups, Izv. Akad. Nauk SSSR Ser. Mat. 35 (1971), 1225–1236 (Russian). MR 0296168
- Irving Kaplansky, Fields and rings, University of Chicago Press, Chicago, Ill.-London, 1969. MR 0269449
- Olav Arnfinn Laudal, Note on the projective limit on small categories, Proc. Amer. Math. Soc. 33 (1972), 307–309. MR 291241, DOI 10.1090/S0002-9939-1972-0291241-8
- Barry Mitchell, Rings with several objects, Advances in Math. 8 (1972), 1–161. MR 294454, DOI 10.1016/0001-8708(72)90002-3
- William R. Nico, A counterexample in the cohomology of monoids, Semigroup Forum 4 (1972), 93–94. MR 311827, DOI 10.1007/BF02570775
- Richard G. Swan, Groups of cohomological dimension one, J. Algebra 12 (1969), 585–610. MR 240177, DOI 10.1016/0021-8693(69)90030-1
- K. Varadarajan, Dimension, category and $K(\pi ,\,n)$ spaces, J. Math. Mech. 10 (1961), 755–771. MR 0126848
Additional Information
- © Copyright 1980 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 80 (1980), 547-551
- MSC: Primary 18G20; Secondary 20M50
- DOI: https://doi.org/10.1090/S0002-9939-1980-0587924-7
- MathSciNet review: 587924