The Journal of the Indian Mathematical Society

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On Some Algebras of Infinite Cohomological Dimension


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1 Tata Institute of Fundamental Research, Bombay, India
     

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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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  • On Some Algebras of Infinite Cohomological Dimension

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Authors

R. Sridharan
Tata Institute of Fundamental Research, Bombay, India

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.