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Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, 2012, Number 2, Pages 59–73
(Mi basm316)
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This article is cited in 2 scientific papers (total in 2 papers)
On partial inverse operations in the lattice of submodules
A. I. Kashu Institute of Mathematics and Computer Science, Academy of Sciences of Moldova, Chişinău, Moldova
Abstract:
In the present work two partial operations in the lattice of submodules $\boldsymbol L(_RM)$ are defined and investigated. They are the inverse operations for $\omega$-product and $\alpha$-coproduct studied in [6]. This is the continuation of the article [7], in which the similar questions for the operations of $\alpha$-product and $\omega$-coproduct are investigated.
The partial inverse operation of left quotient $N\,/_\odot\,K$ of $N$ by $K$ with respect to $\omega$-product is introduced and similarly the right quotient $N\,_:\backslash\,K$ of $K$ by $N$ with respect to $\alpha$-coproduct is defined, where $N,K\in\boldsymbol L(_RM)$. The criteria of existence of such quotients are indicated, as well as the different forms of representation, the main properties, the relations with lattice operations in $\boldsymbol L(_RM)$, the conditions of cancellation and other related questions are elucidated.
Keywords and phrases:
ring, module, lattice, preradical, (co)product of preradical, left (right) quotient of submodules.
Received: 15.05.2012
Citation:
A. I. Kashu, “On partial inverse operations in the lattice of submodules”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2012, no. 2, 59–73
Linking options:
https://www.mathnet.ru/eng/basm316 https://www.mathnet.ru/eng/basm/y2012/i2/p59
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Abstract page: | 265 | Full-text PDF : | 42 | References: | 27 | First page: | 1 |
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