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.