The large condition for rings with Krull dimension

Author:
Ann K. Boyle

Journal:
Proc. Amer. Math. Soc. **72** (1978), 27-32

MSC:
Primary 16A55

DOI:
https://doi.org/10.1090/S0002-9939-1978-0503524-X

MathSciNet review:
503524

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Abstract: A module *M* with Krull dimension is said to satisfy the large condition if for any essential submodule *L* of *M*, the Krull dimension of is strictly less than the Krull dimension of *M*. For a right noetherian ring *R* with Krull dimension this is equivalent to the condition that every f.g. uniform submodule of with Krull dimension is critical. It is also shown that if *R* is right noetherian with Krull dimension and if is a right ideal maximal with respect to *K* , then *R* satisfies the large condition if and only if is a finite intersection of cocritical right ideals and is closed.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1978-0503524-X

Keywords:
The large condition,
semicritical module,
semiprime ring,
nonsingularly *k*-primitive ring

Article copyright:
© Copyright 1978
American Mathematical Society