Let R a commutative semiring with identity. An ideal I is called a multiplication ideal if every ideal contained in I is a multiple of I. We consider the associated ideal theta(I). It is proved that the strong ideal theta(I) is important in the study of multiplication ideals. Among various applications given, the following results are proved: if I is a faithful very strong multiplication ideal, then the strong ideal theta(I) is an idempotent ideal of R such that theta(theta(I)) = theta(I), and every secondary representable ideal of R which is also a very strong multiplication ideal is finitely generated.
展开▼
