Rings and Categories of Modules

Anderson, F. W., & Fuller, K. R. (1992). Rings and Categories of Modules. Springer-Verlag.

Type

Book

Intellectual base

Review or monograph

Year

1992

DOI

10.1007/978-1-4612-4418-9

ISBN

9781461287636

DOI registrant

Springer Nature

Link

https://doi.org/10.1007/978-1-4612-4418-9

Cited by

3 citations across 3 artifacts.

Each citation links to the sentence it supports in the citing article.

Domain-specific

• Idempotent (ring theory)
  • A ring idempotent is unchanged when multiplied by itself.
• 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.

• Perfect ring
  • A perfect ring is characterized by universal availability of minimal projective approximations for modules.

Verification

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