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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
In particular, we study uniqueness and some other properties of such factorizations and investigate the behavior of these factorizations under direct sum and product of rings and modules.
📌 3 Key Takeaways
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Objective & Hypothesis:In this paper, we consider factorizations of elements of a divisor-closed multiplicative submonoid of a ring and also factorizations of elements of a module as a product of elements coming from a divisor-closed multiplicative submonoid of the ring and another element of the module.
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Key Findings & Data:In this paper, we consider factorizations of elements of a divisor-closed multiplicative submonoid of a ring and also factorizations of elements of a module as a product of elements coming from a divisor-closed multiplicative submonoid of the ring and another element of the module.
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Conclusion & Impact:In particular, we study uniqueness and some other properties of such factorizations and investigate the behavior of these factorizations under direct sum and product of rings and modules.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Unique factorization · bounded factorization · primitive elements
Abstract
In this paper, we consider factorizations of elements of a divisor-closed multiplicative submonoid of a ring and also factorizations of elements of a module as a product of elements coming from a divisor-closed multiplicative submonoid of the ring and another element of the module. In particular, we study uniqueness and some other properties of such factorizations and investigate the behavior of these factorizations under direct sum and product of rings and modules.
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Cite This Article
NIKSERESHT, A., AZIZI, A. (2017). Factorization with respect to a divisor-closed multiplicative submonoid of a ring. Turkish Journal of Mathematics, Cilt: 41 - Sayı: 3, 483–499. https://ajindex.com/articles/723188