Glasnik matematički, Vol. 45 No. 2, 2010.
Izvorni znanstveni članak
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
Sažetak
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.
Ključne riječi
Very strong multiplication ideals; ideal θ (I); secondary ideals
Hrčak ID:
62695
URI
Datum izdavanja:
24.12.2010.
Posjeta: 963 *