2021/01/17 by Sarode, Sachin, Joshi, Vinayak
#06F10 Secondary 06A11 #13C05 #Commutative Algebra (math.AC) #FOS: Mathematics #Primary 13A15
paper · doi:10.48550/arxiv.2101.06667
In this paper, we introduce a concept of \mathfrakX-element with respect to an M-closed set \mathfrakX in multiplicative lattices and study properties of \mathfrakX-elements. For a particular M-closed subset \mathfrakX, we define the concept of r-element, n-element and J-element. These elements generalize the notion of r-ideals, n-ideals and J-ideals of a commutative ring with unity to multiplicative lattices. In fact, we prove that an ideal I of a commutative ring R with unity 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.