Algebras With Vanishing n-Cohomology Groups
Open Access
- 1 June 1954
- journal article
- research article
- Published by Cambridge University Press (CUP) in Nagoya Mathematical Journal
- Vol. 7, 115-131
- https://doi.org/10.1017/s0027763000018110
Abstract
Cohomology theory for (associative) algebras was first established in general higher dimensionalities by G. Hochschild [3], [4], [5]. Algebras with vanishing 1-cohomology groups are separable semisimple algebras ([3], Theorem 4.1). On extending and refining our recent results [6], [8], [12], we establish in the present paper the following: Let n ≧ 2. Let A be an (associative) algebra (of finite rank) possessing a unit element 1 over a field Ω, and N be its radical.Keywords
This publication has 12 references indexed in Scilit:
- On the structure of (M 0)-and (M u)-modulesMathematische Zeitschrift, 1953
- Note on the Cohomology Groups of Associative AlgebrasNagoya Mathematical Journal, 1953
- On Absolutely Segregated Algebras and Relative 3-Cohomology Groups of an AlgebraNagoya Mathematical Journal, 1953
- On Absolutely Segregated AlgebrasNagoya Mathematical Journal, 1953
- On the Cohomology Theory for Associative AlgebrasAmerican Journal of Mathematics, 1952
- Cohomology and representations of associative algebrasDuke Mathematical Journal, 1947
- On the Cohomology Theory for Associative AlgebrasAnnals of Mathematics, 1946
- The Theory of RingsPublished by American Mathematical Society (AMS) ,1943
- Some Studies on Regular Representations, Induced Representations and Modular RepresentationsAnnals of Mathematics, 1938
- On the Regular Representations of AlgebrasProceedings of the National Academy of Sciences, 1937