Generalization of prime ideals in M_n(N) -group Nⁿ

The notion of a matrix nearring over an arbitrary nearring was introduced by (Meldrum and Walt Arch. Math. 47(4): 312–319, 1986). In this paper, we define the notions such as weakly τ-prime (τ= 0 , c, 3 , e) ideals of an N-group G, which are the generalization of the classes of τ-prime ideals of G, and provide suitable examples to distinguish between the two classes. We extend the concept to obtain the one-one correspondence between weakly τ-prime ideals (τ= 0 , c, 3 , e) of N-group (over itself) and those of M_n(N) -group Nⁿ, where M_n(N) is the matrix nearring over the nearring N. Further, we prove the correspondence between weakly 2-absorbing ideals of these classes.