Invertible ideals and Gaussian semirings
Archivum mathematicum, Tome 53 (2017) no. 3, pp. 179-192.

Voir la notice de l'article dans Czech Digital Mathematics Library

In the first section, we introduce the notions of fractional and invertible ideals of semirings and characterize invertible ideals of a semidomain. In section two, we define Prüfer semirings and characterize them in terms of valuation semirings. In this section, we also characterize Prüfer semirings in terms of some identities over its ideals such as $(I + J)(I \cap J) = IJ$ for all ideals $I$, $J$ of $S$. In the third section, we give a semiring version for the Gilmer-Tsang Theorem, which states that for a suitable family of semirings, the concepts of Prüfer and Gaussian semirings are equivalent. At last, we end this paper by giving a plenty of examples for proper Gaussian and Prüfer semirings.
DOI : 10.5817/AM2017-3-179
Classification : 06D75, 13B25, 13F25, 16Y60
Mots-clés : semiring; semiring polynomials; Gaussian semiring; cancellation ideals; invertible ideals 
@article{10_5817_AM2017_3_179,
     author = {Ghalandarzadeh, Shaban and Nasehpour, Peyman and Razavi, Rafieh},
     title = {Invertible ideals and {Gaussian} semirings},
     journal = {Archivum mathematicum},
     pages = {179--192},
     publisher = {mathdoc},
     volume = {53},
     number = {3},
     year = {2017},
     doi = {10.5817/AM2017-3-179},
     mrnumber = {3708771},
     zbl = {06819524},
     language = {en},
     url = {https://geodesic-test.mathdoc.fr/articles/10.5817/AM2017-3-179/}
}
TY  - JOUR
AU  - Ghalandarzadeh, Shaban
AU  - Nasehpour, Peyman
AU  - Razavi, Rafieh
TI  - Invertible ideals and Gaussian semirings
JO  - Archivum mathematicum
PY  - 2017
SP  - 179
EP  - 192
VL  - 53
IS  - 3
PB  - mathdoc
UR  - https://geodesic-test.mathdoc.fr/articles/10.5817/AM2017-3-179/
DO  - 10.5817/AM2017-3-179
LA  - en
ID  - 10_5817_AM2017_3_179
ER  - 
%0 Journal Article
%A Ghalandarzadeh, Shaban
%A Nasehpour, Peyman
%A Razavi, Rafieh
%T Invertible ideals and Gaussian semirings
%J Archivum mathematicum
%D 2017
%P 179-192
%V 53
%N 3
%I mathdoc
%U https://geodesic-test.mathdoc.fr/articles/10.5817/AM2017-3-179/
%R 10.5817/AM2017-3-179
%G en
%F 10_5817_AM2017_3_179
Ghalandarzadeh, Shaban; Nasehpour, Peyman; Razavi, Rafieh. Invertible ideals and Gaussian semirings. Archivum mathematicum, Tome 53 (2017) no. 3, pp. 179-192. doi : 10.5817/AM2017-3-179. https://geodesic-test.mathdoc.fr/articles/10.5817/AM2017-3-179/

Cité par Sources :