Geodesic
Maximal non-pseudovaluation subrings of an integral domain
Czechoslovak Mathematical Journal, Tome 74 (2024) no. 2, pp. 389-395
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

The notion of maximal non-pseudovaluation subring of an integral domain is introduced and studied. Let $R\subset S$ be an extension of domains. Then $R$ is called a maximal non-pseudovaluation subring of $S$ if $R$ is not a pseudovaluation subring of $S$, and for any ring $T$ such that $R \subset T\subset S$, $T$ is a pseudovaluation subring of $S$. We show that if $S$ is not local, then there no such $T$ exists between $R$ and $S$. We also characterize maximal non-pseudovaluation subrings of a local integral domain.
The notion of maximal non-pseudovaluation subring of an integral domain is introduced and studied. Let $R\subset S$ be an extension of domains. Then $R$ is called a maximal non-pseudovaluation subring of $S$ if $R$ is not a pseudovaluation subring of $S$, and for any ring $T$ such that $R \subset T\subset S$, $T$ is a pseudovaluation subring of $S$. We show that if $S$ is not local, then there no such $T$ exists between $R$ and $S$. We also characterize maximal non-pseudovaluation subrings of a local integral domain.
DOI : 10.21136/CMJ.2024.0122-23
Classification : 13B02, 13B22, 13G05
Keywords: maximal non-pseudovaluation domain; pseudovaluation subring 
@article{10_21136_CMJ_2024_0122_23,
     author = {Kumar, Rahul},
     title = {Maximal non-pseudovaluation subrings of an integral domain},
     journal = {Czechoslovak Mathematical Journal},
     pages = {389--395},
     year = {2024},
     volume = {74},
     number = {2},
     doi = {10.21136/CMJ.2024.0122-23},
     mrnumber = {4764529},
     zbl = {07893388},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2024.0122-23/}
}
TY  - JOUR
AU  - Kumar, Rahul
TI  - Maximal non-pseudovaluation subrings of an integral domain
JO  - Czechoslovak Mathematical Journal
PY  - 2024
SP  - 389
EP  - 395
VL  - 74
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2024.0122-23/
DO  - 10.21136/CMJ.2024.0122-23
LA  - en
ID  - 10_21136_CMJ_2024_0122_23
ER  - 
%0 Journal Article
%A Kumar, Rahul
%T Maximal non-pseudovaluation subrings of an integral domain
%J Czechoslovak Mathematical Journal
%D 2024
%P 389-395
%V 74
%N 2
%U http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2024.0122-23/
%R 10.21136/CMJ.2024.0122-23
%G en
%F 10_21136_CMJ_2024_0122_23
Kumar, Rahul. Maximal non-pseudovaluation subrings of an integral domain. Czechoslovak Mathematical Journal, Tome 74 (2024) no. 2, pp. 389-395. doi: 10.21136/CMJ.2024.0122-23

[1] Ayache, A., Echi, O.: Valuation and pseudovaluation subrings of an integral domain. Commun. Algebra 34 (2006), 2467-2483. | DOI | MR | JFM

[2] Ayache, A., Jaballah, A.: Residually algebraic pairs of rings. Math. Z. 225 (1997), 49-65. | DOI | MR | JFM

[3] Cahen, P.-J.: Couple d'anneaux partageant un idéal. Arch. Math. 51 (1988), 505-514 French. | DOI | MR | JFM

[4] Davis, E. D.: Overrings of commutative rings. III. Normal pairs. Trans. Am. Math. Soc. 182 (1973), 175-185. | DOI | MR | JFM

[5] Dechene, L. I.: Adjacent Extensions of Rings: Ph.D. Dissertation. University of California, Riverside (1978). | MR

[6] Dobbs, D. E., Fontana, M.: Universally incomparable ring homomorphisms. Bull. Aust. Math. Soc. 29 (1984), 289-302. | DOI | MR | JFM

[7] Ferrand, D., Olivier, J.-P.: Homomorphismes minimaux d'anneaux. J. Algebra 16 (1970), 461-471 French. | DOI | MR | JFM

[8] Hedstrom, J. R., Houston, E. G.: Pseudo-valuation domains. Pac. J. Math. 75 (1978), 137-147. | DOI | MR | JFM

[9] Jarboui, N., Trabelsi, S.: Some results about proper overrings of pseudo-valuation domains. J. Algebra Appl. 15 (2016), Article ID 1650099, 16 pages. | DOI | MR | JFM

[10] Kumar, R., Gaur, A.: Maximal non valuation domains in an integral domain. Czech. Math. J. 70 (2020), 1019-1032. | DOI | MR | JFM

[11] Modica, M. L.: Maximal Subrings: Ph.D. Dissertation. University of Chicago, Chicago (1975). | MR

Cité par Sources :