Geodesic
Ideal Theory in Commutative Semirings
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2008), pp. 14-23

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper, we analyze some results on ideal theory of commutative semirings with non-zero identity analogues to commutative rings with non-zero identity. Here we will make an intensive examination of the notions of Noetherian semirings, Artinian semirings, local semirings and strongly irreducible ideals in commutative semirings. It is shown that this notion inherits most of essential properties of strongly irreducible ideals of a commutative rings with non-zero identity. Also, the relationship among the families of primary ideals, irreducible ideals and strongly irreducible ideals of a semiring $R$ is considered. 
@article{BASM_2008_2_a1,
     author = {Reza Ebrahim Atani and Shahabaddin Ebrahimi Atani},
     title = {Ideal {Theory} in {Commutative} {Semirings}},
     journal = {Buletinul Academiei de \c{S}tiin\c{t}e a Republicii Moldova. Matematica},
     pages = {14--23},
     publisher = {mathdoc},
     number = {2},
     year = {2008},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BASM_2008_2_a1/}
}
TY  - JOUR
AU  - Reza Ebrahim Atani
AU  - Shahabaddin Ebrahimi Atani
TI  - Ideal Theory in Commutative Semirings
JO  - Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
PY  - 2008
SP  - 14
EP  - 23
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/BASM_2008_2_a1/
LA  - en
ID  - BASM_2008_2_a1
ER  - 
%0 Journal Article
%A Reza Ebrahim Atani
%A Shahabaddin Ebrahimi Atani
%T Ideal Theory in Commutative Semirings
%J Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
%D 2008
%P 14-23
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/BASM_2008_2_a1/
%G en
%F BASM_2008_2_a1
Reza Ebrahim Atani; Shahabaddin Ebrahimi Atani. Ideal Theory in Commutative Semirings. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2008), pp. 14-23. http://geodesic.mathdoc.fr/item/BASM_2008_2_a1/