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Maximal non-valuative domains.
- Source :
-
Proceedings of the Indian Academy of Sciences: Mathematical Sciences . Jun2024, Vol. 134 Issue 1, p1-12. 12p. - Publication Year :
- 2024
-
Abstract
- The notion of maximal non-valuative domain is introduced and characterized. An integral domain R is called a maximal non-valuative domain if R is not a valuative domain but every proper overring of R is a valuative domain. Maximal non-valuative domains have at most four maximal ideals. Various properties of maximal non-valuative domains are discussed. We characterize integrally closed maximal non-valuative domains in terms of B e ´ zout domains. A local non-integrally closed maximal non-valuative domain is also characterized. Conditions are given under which pseudo-valuation domains and maximal non-pseudo-valuation domains are maximal non-valuative domains. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 02534142
- Volume :
- 134
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Proceedings of the Indian Academy of Sciences: Mathematical Sciences
- Publication Type :
- Academic Journal
- Accession number :
- 176660415
- Full Text :
- https://doi.org/10.1007/s12044-024-00781-7