On 2-absorbing and Weakly 2-absorbing Ideals in Product Lattices

摘要

In this paper, we study some properties of 2-absorbing and weakly 2-absorbing ideals in the direct product of lattices. We show that for proper ideals I_1 and I2 of L_1 and L2 respectively, if I =I_1 × I_2 is a 2-absorbing ideal of L = L_1 × L_2, then I_1 and I2 are 2-absorbing ideals of L_1 and L2 respectively. We prove this property for weakly 2-absorbing ideals also. We give some characterizations of 2-absorbing and weakly 2-absorbing ideals in the direct product of lattices.