On Some Algebras of Infinite Cohomological Dimension

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Authors

  • Tata Institute of Fundamental Research, Bombay ,IN

DOI:

https://doi.org/10.18311/jims/1957/16967

Abstract

If A is a nilpotent algebra of finite rank over afield K, the cohomological dimension of A is greater than or equal to 3.

We prove here that the dimension is actually infinite. As a consequence, we deduce that the cohomological dimension of the Grassmann ring on n-letters over a commutative semi-simple ring is infinite. This provides, incidentally, counter-examples to certain questions in Homological Algebra.

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Published

1957-12-01

How to Cite

Sridharan, R. (1957). On Some Algebras of Infinite Cohomological Dimension. The Journal of the Indian Mathematical Society, 21(3-4), 179–183. https://doi.org/10.18311/jims/1957/16967