ON VARIOUS CLASSES OF ONE-SIDED IDEALS IN b-SEMIRINGS

. In this paper, we introduce weak-1 right(left) ideals, weak-2 right(left) ideals, weak-1 ideals and weak-2 ideals of b-semirings. We characterize the U product and 0 product of various classes of weak ideals with right ideals and the U product and 0 product of various classes of left ideals with weak ideals. We establish the sufficient conditions for Upsilon U D to be a weak-2 ideal and a right ideal whenever D is a right ideal, respectively. Various sufficient conditions for Upsilon 0 D to be a weak-1 right ideal are established whenever D is a right ideal. To prove that the U product of left ideal and right ideal is a weak-2 ideal, also the 0 product of left ideal and right ideal is a weak-1 ideal. We establish the sufficient conditions for Upsilon U D to be a weak-2 ideal and a left ideal whenever Upsilon is a left ideal, respectively. Various sufficient conditions for Upsilon 0 D to be a weak-1 ideal are established whenever Upsilon is a left ideal. A weak-2 right ideal that need not be an ideal is exemplified by the U product of left ideals instance. Also, the 0 product of left ideals with a weak-2 right ideal need not be a weak-1 ideal of b-semirings.