W. Żelazko (2000)
Studia Mathematica
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Let A be a commutative unital Fréchet algebra, i.e. a completely metrizable topological algebra. Our main result states that all ideals in A are closed if and only if A is a noetherian algebra
Celestin Lele, Salissou Moutari (2006)
Discussiones Mathematicae - General Algebra and Applications
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This paper deals with some properties of n-fold commutative ideals and n-fold weak commutative ideals in BCK-algebras. Afterwards, we construct some algorithms for studying foldness theory of commutative ideals in BCK-algebras.
Chenglong Wu, Yuzhong Ding (2008)
Formalized Mathematics
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In this article three classes of ideals are discussed: associative ideals, commutative ideals, implicative ideals and positive implicative ideals, and their elementary properties. Some of their properties and the relationships between them have not been proven yet, and will be completed in the following article.MML identifier: BCIIDEAL, version: 7.8.10 4.99.1005
Abujabal, H.A.S., Aslam, M., Thaheem, A.B. (1996)
International Journal of Mathematics and Mathematical Sciences
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Weinert, H.J., Sen, M.K., Adhikari, M.R. (1996)
Mathematica Pannonica
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H. A. S. Abujabal, M. A. Obaid, M. Aslam, Allah-Bakhsh Thaheem (1995)
Czechoslovak Mathematical Journal
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Ali, Majid M. (1996)
Beiträge zur Algebra und Geometrie
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S. Bourne (1963)
Studia Mathematica
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Kondo, Michiro (2001)
International Journal of Mathematics and Mathematical Sciences
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Young Bae Jun, Eun Hwan Roh, Seok Zun Song (2016)
Bulletin of the Section of Logic
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The notions of a C-energetic subset and (anti) permeable C-value in BCK-algebras are introduced, and related properties are investigated. Conditions for an element t in [0, 1] to be an (anti) permeable C-value are provided. Also conditions for a subset to be a C-energetic subset are discussed. We decompose BCK-algebra by a partition which consists of a C-energetic subset and a commutative ideal.
Keiji Izuchi (1976)
Studia Mathematica
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Antoni Wawrzyńczyk (2000)
Studia Mathematica
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The class ω(A) of ideals consisting of topological zero divisors of a commutative Banach algebra A is studied. We prove that the maximal ideals of the class ω(A) are of codimension one.
S. Ebrahimi Atani, M. Shajari Kohan, Z. Ebrahimi Sarvandi (2014)
Discussiones Mathematicae - General Algebra and Applications
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In this paper, specifically, we look at the preservation of the diameter and girth of the zero-divisor graph with respect to an ideal of a commutative ring when extending to a finite direct product of commutative rings.