The large condition for rings with Krull dimension
1978; American Mathematical Society; Volume: 72; Issue: 1 Linguagem: Inglês
10.1090/s0002-9939-1978-0503524-x
ISSN1088-6826
Autores Tópico(s)Algebraic structures and combinatorial models
ResumoA module M with Krull dimension is said to satisfy the large condition if for any essential submodule L of M , the Krull dimension of M / L M/L is strictly less than the Krull dimension of M . For a right noetherian ring R with Krull dimension α \alpha this is equivalent to the condition that every f.g. uniform submodule of E ( R R ) E({R_R}) with Krull dimension α \alpha is critical. It is also shown that if R is right noetherian with Krull dimension α \alpha and if I 0 {I_0} is a right ideal maximal with respect to K dim I 0 > α \dim {I_0} > \alpha , then R satisfies the large condition if and only if I 0 {I_0} is a finite intersection of cocritical right ideals and I 0 {I_0} is closed.
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