Rings and Categories of Modules¶
Anderson, F. W., & Fuller, K. R. Rings and Categories of Modules. Graduate Texts in Mathematics.
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Domain-specific¶
- Maximal Ideal
- Therefore \(\mathfrak m\) is maximal exactly when the nonzero quotient \(R/\mathfrak m\) has no nonzero proper two-sided ideals—that is, when the quotient is a simple ring.
This sourceGraduate Texts in Mathematics 13. Springer, 1992. Authoritative source for ideals, modules, simple quotients, one-sided ideal structure, and the relation between rings and module categories.
- Therefore \(\mathfrak m\) is maximal exactly when the nonzero quotient \(R/\mathfrak m\) has no nonzero proper two-sided ideals—that is, when the quotient is a simple ring.
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