Original scientific paper

https://doi.org/10.3336/gm.45.2.07

Very strong multiplication ideals and the ideal θ(I) over a commutative semirings

Shahabaddin Ebrahimi Atani ; Department of Mathematics, University of Guilan, P.O. Box 1914, Rasht, Iran
Reza Ebrahimi Atani ; Department of Electrical Engineering, University of Guilan, P.O.Box 3756, Rasht, Iran

Abstract

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 θ(I). It is proved that the strong ideal θ(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 θ(I) is an idempotent ideal of R such that θ(θ(I)) = θ(I), and every secondary representable ideal of R which is also a very strong multiplication ideal is finitely generated.

Keywords

Very strong multiplication ideals; ideal θ (I); secondary ideals

Hrčak ID:

62695

URI

https://hrcak.srce.hr/62695

Publication date:

24.12.2010.

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