ON DIMENSION OF THE SPACE OF DERIVATIONS ON COMMUTATIVE REGULAR ALGEBRAS

The present paper is devoted to the study of the dimension of the space of all derivations on homogeneous commutative regular algebras. We shall show that if Ω , Σ , μ is a Maharam homogeneous measure space with a finite countable-additive measure μ and A is a homogeneous regular unital subalgebra i...

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Bibliographic Details
Published in:Journal of mathematical sciences (New York, N.Y.) N.Y.), 2023-04, Vol.271 (6), p.694-699
Main Authors: Ayupov, Shavkat, Kudaybergenov, Karimbergen, Karimov, Khakimbek
Format: Article
Language:English
Subjects:
Algebra
Boolean algebra
Mathematics
Mathematics and Statistics
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Summary:The present paper is devoted to the study of the dimension of the space of all derivations on homogeneous commutative regular algebras. We shall show that if Ω , Σ , μ is a Maharam homogeneous measure space with a finite countable-additive measure μ and A is a homogeneous regular unital subalgebra in S ( Ω ) with the homogeneous Boolean algebra of idempotents ∇ ( A ) , then dim Der ( A ) = τ ( ∇ ( A ) ) trdeg ( A ) , where τ ( ∇ ( A ) ) is the weight of the Boolean algebra ∇ ( A ) and trdeg ( A ) is the transcendence degree of A .
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-023-06577-w