scholarly journals On Cohomology Groups of Four-Dimensional Nilpotent Associative Algebras

2021 ◽  
Vol 19 (2) ◽  
Keyword(s):  
Cohomology Groups ◽  
Associative Algebras

scholarly journals Note on the Cohomology Groups of Associative Algebras

1953 ◽  
Vol 6 ◽  
pp. 85-92 ◽  
Author(s):  
Hirosi Nagao
Keyword(s):  
Detailed Analysis ◽  
Structural Characterization ◽  
Cohomology Theory ◽  
Cohomology Groups ◽  
Associative Algebras ◽  
3 Dimensional

The cohomology theory of associative algebras has been developed by G. liochschild [1], [2], [3], and the 1-, 2-, and 3-dimensional cohomology groups have been interpreted with reference to classical notions of structure in his papers. Recently M. Ikeda has obtained, by a detailed analysis of Hochschild’s modules, an interesting structural characterization of the class of algebras whose 2-dimensional cohomology groups are all zero [5].

ON COHOMOLOGY GROUPS OF THREE-DIMENSIONAL COMPLEX ASSOCIATIVE ALGEBRAS

2017 ◽  
Vol 102 (4) ◽  
pp. 669-686
Author(s):  
N. F. Mohammed ◽  
I. S. Rakhimov ◽  
Sh. K. Said Husain
Keyword(s):  
Three Dimensional ◽  
Cohomology Groups ◽  
Associative Algebras

scholarly journals Algebras With Vanishing n-Cohomology Groups

1954 ◽  
Vol 7 ◽  
pp. 115-131 ◽  
Author(s):  
Masatoshi Ikeda ◽  
Hiroshi Nagao ◽  
Tadashi Nakayama
Keyword(s):  
Associative Algebra ◽  
Finite Rank ◽  
Unit Element ◽  
Cohomology Theory ◽  
Cohomology Groups ◽  
Associative Algebras ◽  
Semisimple Algebras

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.

scholarly journals On Absolutely Segregated Algebras

1953 ◽  
Vol 6 ◽  
pp. 63-75 ◽  
Author(s):  
Masatoshi Ikeda
Keyword(s):  
Higher Dimensions ◽  
Cohomology Groups ◽  
Associative Algebras ◽  
3 Dimensional ◽  
Separable Algebras

Cohomology groups of (associative) algebras have been introduced (for higher dimensions) and studied by G. Hochschild in his papers [2], [3] and [4]. 1-, 2-, and 3-dimensional cohomology groups are in closest connection with some classical properties of algebras. In particular, an algebra is absolutely segregated. if and only if its 2-dimensional cohomology groups are all trivial. It is thus of use and importance to determine the structure of algebras with universally vanishing 2-cohomology groups, i.e. absolutely segregated algebras; they form a class which is wider than the class of all algebras with universally vanishing 1-cohomology groups, i.e. separable algebras in the sense of the Dickson-Wed-derburn theorem.

Extensions of Lie Algebras and the Third Cohomology Group

1953 ◽  
Vol 5 ◽  
pp. 470-476 ◽  
Author(s):  
S. I. Goldberg
Keyword(s):  
Lie Algebra ◽  
Lie Algebras ◽  
Cohomology Group ◽  
Algebraic Structures ◽  
Cohomology Groups ◽  
Associative Algebras ◽  
The Third

Cohomology theories of various algebraic structures have been investigated by several authors. The most noteworthy are due to Hochschild, MacLane and Eckmann, Chevalley and Eilenberg, who developed the theory of cohomology groups of associative algebras, abstract groups, and Lie algebras respectively. In this paper we are concerned primarily with a characterization of the third cohomology group of a Lie algebra by its extension properties.

scholarly journals Total Differentiability and Monogenicity for Functions in Algebras of Order 4

2021 ◽  
Vol 15 (2) ◽  
Author(s):  
I. Sabadini ◽  
D. C. Struppa
Keyword(s):  
Analytic Functions ◽  
Associative Algebras ◽  
Basic Tool ◽  
Algebraic Analysis ◽  
Italian School ◽  
Relevant Role

AbstractIn this paper we discuss some notions of analyticity in associative algebras with unit. We also recall some basic tool in algebraic analysis and we use them to study the properties of analytic functions in two algebras of dimension four that played a relevant role in some work of the Italian school, but that have never been fully investigated.

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