A Study of NeutroAlgebra and AntiAlgebra of Ideals in a Factor Ring

Abstract

If I is an ideal in a ring R and M is the collection of all nontrivial ideals in the factor ring R/I, we find in this paper conditions under which (M, ⊕), (M, ⊗) and (M, ∩) are NeutroAlgebras and AntiAlgebras where ⊕, ⊗ and ∩ are the usual sum, product and intersection of ideals in R/I.

Keywords

• classicalalgebra
• partialalgebra. neutroalgebra
• antialgebra
• neutrosubalgebra
• sum of ideals
• product of ideals
• intersection of ideals