A ring with identity is said to be a local ring if it contains a unique maximal right ideal [2; 751. This implies that the unique maximal right ideal is also the unique maximal ideal. But rings with unique maximal ideals need not be local rings. The ring of all 2x2 matrices over the ring of integers
Invariant maximal ideals of commutative rings
β Scribed by B.A.F Wehrfritz
- Publisher
- Elsevier Science
- Year
- 1979
- Tongue
- English
- Weight
- 496 KB
- Volume
- 56
- Category
- Article
- ISSN
- 0021-8693
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## Abstract In this work we introduce a class of commutative rings whose defining condition is that its lattice of ideals, augmented with the ideal product, the semiβring of ideals, is isomorphic to an MVβalgebra. This class of rings coincides with the class of commutative rings which are direct su
We introduce and impose conditions under which the finitely generated essential right ideals of E may be classified in terms of k-submodules of M. This yields a classification of the domains Morita equivalent to E when E is a Noetherian domain. For example, a special case of our results is: