ON (n . 1, n)-φ-PRIME IDEALS IN SEMIRINGS

摘要

Let S be a commutative semiring and T (S) be the set of all ideals of S. Let φ : T (S) → T (S)∪ {.} be a function. A proper ideal I of a semiring S is called an (n.1, n)-φ-prime ideal of S if a 1 a 2 · · · a n ∈ I φ(I), a 1 , a 2 , . . . , a n ∈ S implies that a 1 a 2 · · · a i.1 a i+1 · · · a n ∈ I for some i ∈ {1, 2, . . . , n}. In this paper, we prove several results concerning (n . 1, n)-φ-prime ideals in a commutative semiring S with non-zero identity connected with those in commutative ring theory.