Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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THE DIMENSION OF THE MAXIMAL SPECTRUM OF SOME RING EXTENSIONS

  • Rachida, El Khalfaoui (Mathematical Sciences and Applications Laboratory Department of Mathematics Faculty of Sciences Dhar Al Mahraz) ;
  • Najib Mahdou (Laboratory of Modeling and Mathematical Structures Department of Mathematics Faculty of Science and Technology of Fez Box 2202, University S.M. Ben Abdellah)
  • Received : 2022.11.13
  • Accepted : 2022.12.23
  • Published : 2023.10.31
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Abstract

Let A be a ring and 𝓙 = {ideals I of A | J(I) = I}. The Krull dimension of A, written dim A, is the sup of the lengths of chains of prime ideals of A; whereas the dimension of the maximal spectrum, denoted by dim 𝓙A, is the sup of the lengths of chains of prime ideals from 𝓙. Then dim 𝓙A ≤ dim A. In this paper, we will study the dimension of the maximal spectrum of some constructions of rings and we will be interested in the transfer of the property J-Noetherian to ring extensions.

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Acknowledgement

The authors would like to express their sincere thanks for the referee for his/her helpful suggestions and comments.

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