ON DIMENSION OF THE SPACE OF DERIVATIONS ON COMMUTATIVE REGULAR ALGEBRAS

Shavkat Ayupov; Karimbergen Kudaybergenov; Khakimbek Karimov

doi:10.1007/s10958-023-06577-w

ON DIMENSION OF THE SPACE OF DERIVATIONS ON COMMUTATIVE REGULAR ALGEBRAS

Shavkat Ayupov
, Karimbergen Kudaybergenov^*
, Khakimbek Karimov

^*Corresponding author for this work

Academy of Sciences of the Republic of Uzbekistan
National University of Uzbekistan named after Mirzo Ulugbek
North Caucasus Center for Mathematical Research
Karakalpak State University

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

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 dimDer(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.

Original language	English
Pages (from-to)	694-699
Number of pages	6
Journal	Journal of Mathematical Sciences (United States)
Volume	271
Issue number	6
DOIs	https://doi.org/10.1007/s10958-023-06577-w
State	Published - Apr 2023
Externally published	Yes

Keywords

16E50
47B47
Algebra of measurable functions
Derivation
Homogeneous commutative regular algebra
Maharam measure space

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10.1007/s10958-023-06577-w

Cite this

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title = "ON DIMENSION OF THE SPACE OF DERIVATIONS ON COMMUTATIVE REGULAR ALGEBRAS",

abstract = "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 dimDer(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.",

keywords = "16E50, 47B47, Algebra of measurable functions, Derivation, Homogeneous commutative regular algebra, Maharam measure space",

author = "Shavkat Ayupov and Karimbergen Kudaybergenov and Khakimbek Karimov",

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N1 - Publisher Copyright: © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2023.

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AB - 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 dimDer(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.

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ON DIMENSION OF THE SPACE OF DERIVATIONS ON COMMUTATIVE REGULAR ALGEBRAS

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Keywords

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