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 $R$.
Sarode, S., & Joshı, V. (2022). $\mathfrak{X}$-elements in multiplicative lattices - A generalization of $J$-ideals, $n$-ideals and $r$-ideals in rings. International Electronic Journal of Algebra, 32(32), 46-61. https://doi.org/10.24330/ieja.1102289
AMA
Sarode S, Joshı V. $\mathfrak{X}$-elements in multiplicative lattices - A generalization of $J$-ideals, $n$-ideals and $r$-ideals in rings. IEJA. July 2022;32(32):46-61. doi:10.24330/ieja.1102289
Chicago
Sarode, Sachin, and Vinayak Joshı. “$\mathfrak{X}$-Elements in Multiplicative Lattices - A Generalization of $J$-Ideals, $n$-Ideals and $r$-Ideals in Rings”. International Electronic Journal of Algebra 32, no. 32 (July 2022): 46-61. https://doi.org/10.24330/ieja.1102289.
EndNote
Sarode S, Joshı V (July 1, 2022) $\mathfrak{X}$-elements in multiplicative lattices - A generalization of $J$-ideals, $n$-ideals and $r$-ideals in rings. International Electronic Journal of Algebra 32 32 46–61.
IEEE
S. Sarode and V. Joshı, “$\mathfrak{X}$-elements in multiplicative lattices - A generalization of $J$-ideals, $n$-ideals and $r$-ideals in rings”, IEJA, vol. 32, no. 32, pp. 46–61, 2022, doi: 10.24330/ieja.1102289.
ISNAD
Sarode, Sachin - Joshı, Vinayak. “$\mathfrak{X}$-Elements in Multiplicative Lattices - A Generalization of $J$-Ideals, $n$-Ideals and $r$-Ideals in Rings”. International Electronic Journal of Algebra 32/32 (July 2022), 46-61. https://doi.org/10.24330/ieja.1102289.
JAMA
Sarode S, Joshı V. $\mathfrak{X}$-elements in multiplicative lattices - A generalization of $J$-ideals, $n$-ideals and $r$-ideals in rings. IEJA. 2022;32:46–61.
MLA
Sarode, Sachin and Vinayak Joshı. “$\mathfrak{X}$-Elements in Multiplicative Lattices - A Generalization of $J$-Ideals, $n$-Ideals and $r$-Ideals in Rings”. International Electronic Journal of Algebra, vol. 32, no. 32, 2022, pp. 46-61, doi:10.24330/ieja.1102289.
Vancouver
Sarode S, Joshı V. $\mathfrak{X}$-elements in multiplicative lattices - A generalization of $J$-ideals, $n$-ideals and $r$-ideals in rings. IEJA. 2022;32(32):46-61.