Complex algebras of subalgebras

K. Adaricheva; A. Pilitowska; D. Stanovský

doi:10.1007/s10469-008-9036-7

Complex algebras of subalgebras

K. Adaricheva, A. Pilitowska, D. Stanovský

Department of Mathematics

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

6 Citations (Scopus)

Abstract

Let V be a variety of algebras. We specify a condition (the so-called generalized entropic property), which is equivalent to the fact that for every algebra A V, the set of all subalgebras of A is a subuniverse of the complex algebra of the subalgebras of A. The relationship between the generalized entropic property and the entropic law is investigated. Also, for varieties with the generalized entropic property, we consider identities that are satisfied by complex algebras of subalgebras.

Original language	English
Pages (from-to)	367-383
Number of pages	17
Journal	Algebra and Logic
Volume	47
Issue number	6
DOIs	https://doi.org/10.1007/s10469-008-9036-7
Publication status	Published - Nov 2008

Keywords

Complex algebra
Complex algebra of subalgebras
Entropic law
Linear identity
Mediality
Mode

ASJC Scopus subject areas

Analysis
Logic

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title = "Complex algebras of subalgebras",

abstract = "Let V be a variety of algebras. We specify a condition (the so-called generalized entropic property), which is equivalent to the fact that for every algebra A V, the set of all subalgebras of A is a subuniverse of the complex algebra of the subalgebras of A. The relationship between the generalized entropic property and the entropic law is investigated. Also, for varieties with the generalized entropic property, we consider identities that are satisfied by complex algebras of subalgebras.",

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note = "Funding Information: ∗Supported by INTAS grant No. 03-51-4110. ∗∗Supported by MSˇMTCˇR (project MSM 0021620839) No. 201/05/0002).",

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T1 - Complex algebras of subalgebras

AU - Adaricheva, K.

AU - Pilitowska, A.

AU - Stanovský, D.

N1 - Funding Information: ∗Supported by INTAS grant No. 03-51-4110. ∗∗Supported by MSˇMTCˇR (project MSM 0021620839) No. 201/05/0002).

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N2 - Let V be a variety of algebras. We specify a condition (the so-called generalized entropic property), which is equivalent to the fact that for every algebra A V, the set of all subalgebras of A is a subuniverse of the complex algebra of the subalgebras of A. The relationship between the generalized entropic property and the entropic law is investigated. Also, for varieties with the generalized entropic property, we consider identities that are satisfied by complex algebras of subalgebras.

AB - Let V be a variety of algebras. We specify a condition (the so-called generalized entropic property), which is equivalent to the fact that for every algebra A V, the set of all subalgebras of A is a subuniverse of the complex algebra of the subalgebras of A. The relationship between the generalized entropic property and the entropic law is investigated. Also, for varieties with the generalized entropic property, we consider identities that are satisfied by complex algebras of subalgebras.

KW - Complex algebra

KW - Complex algebra of subalgebras

KW - Entropic law

KW - Linear identity

KW - Mediality

KW - Mode

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