Geodesic
Right Quotient Rings of a Right LCM Domain
Canadian journal of mathematics, Tome 24 (1972) no. 5, pp. 983-988

Voir la notice de l'article provenant de la source Cambridge University Press

In this paper we continue our investigation of the class of right LCM domains which was introduced in [2]. A right LCM domain is an (not necessarily commutative) integral domain with unity in which the intersection of any two principal right ideals is again principal. In this note we study the right quotient rings of such a ring. In Section 1 we describe some of the characteristic properties of right quotient monoids with respect to which quotient rings are formed. Three particular types of quotient rings are described in Section 2. In Section 3 we relate the right ideals of a ring to those of its quotient ring. 
Beauregard, Raymond A. Right Quotient Rings of a Right LCM Domain. Canadian journal of mathematics, Tome 24 (1972) no. 5, pp. 983-988. doi: 10.4153/CJM-1972-099-3
@article{10_4153_CJM_1972_099_3,
     author = {Beauregard, Raymond A.},
     title = {Right {Quotient} {Rings} of a {Right} {LCM} {Domain}},
     journal = {Canadian journal of mathematics},
     pages = {983--988},
     year = {1972},
     volume = {24},
     number = {5},
     doi = {10.4153/CJM-1972-099-3},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1972-099-3/}
}
TY  - JOUR
AU  - Beauregard, Raymond A.
TI  - Right Quotient Rings of a Right LCM Domain
JO  - Canadian journal of mathematics
PY  - 1972
SP  - 983
EP  - 988
VL  - 24
IS  - 5
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1972-099-3/
DO  - 10.4153/CJM-1972-099-3
ID  - 10_4153_CJM_1972_099_3
ER  - 
%0 Journal Article
%A Beauregard, Raymond A.
%T Right Quotient Rings of a Right LCM Domain
%J Canadian journal of mathematics
%D 1972
%P 983-988
%V 24
%N 5
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1972-099-3/
%R 10.4153/CJM-1972-099-3
%F 10_4153_CJM_1972_099_3

[1] 1. Beauregard, R. A., Infinite primes and unique factorization in a principal right ideal domain, Trans. Amer. Math. Soc. 141 (1969), 245–254. Google Scholar

[2] 2. Beauregard, R. A., Right LCM domains, Proc. Amer. Math. Soc. 30 (1971), 1–7. Google Scholar

[3] 3. Brungs, H. H., Ringe mit eindeutiger Faktorzerlegung, J. Reine Angew. Math. 236 (1969), 43–66. Google Scholar

[4] 4. Jacobson, N., The theory of rings, Math. Surveys No. II, Amer. Math. Soc., 1943. Google Scholar

Cité par Sources :