$\mathfrak{X}$-elements in multiplicative lattices - A generalization of $J$-ideals, $n$-ideals and $r$-ideals in rings
| Autor: | Sachin SARODE, Vinayak JOSHİ |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
$\mathfrak{X}$-element
$n$-element $r$-element $n$-ideal $r$-ideal $J$-ideal $J$-element Multiplicative lattice prime element commutative ring Matematik Algebra and Number Theory Mathematics::Commutative Algebra FOS: Mathematics Mathematics - Commutative Algebra Commutative Algebra (math.AC) Primary 13A15 13C05 06F10 Secondary 06A11 Mathematics |
| Zdroj: | Volume: 32, Issue: 32 46-61 International Electronic Journal of Algebra |
| ISSN: | 1306-6048 |
| Popis: | In this paper, we introduce the concept of an $\mathfrak{X}$-element with respect to an $M$-closed set $\mathfrak{X}$ in multiplicative lattices and study properties of $\mathfrak{X}$-elements. For a particular $M$-closed subset $\mathfrak{X}$, we define the concepts of $r$-elements, $n$-elements and $J$-elements. These elements generalize the notion of $r$-ideals, $n$-ideals and $J$-ideals of a commutative ring with identity to multiplicative lattices. In fact, we prove that an ideal $I$ of a commutative ring $R$ with identity is a $n$-ideal ($J$-ideal) of $R$ if and only if it is an $n$-element ($J$-element) of $Id(R)$, the ideal lattice of $R$. |
| Databáze: | OpenAIRE |
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