On nonnil-u-S-coherent rings
Najib Mahdou\,^1 and El Houssaine Oubouhou\,^2
\,^{1,2}Department of Mathematics, Faculty of Science and Technology of Fez, Box 2202, University S.M. Ben Abdellah Fez, Morocco.
Pages 138-151 | Received 20 November 2024, Accepted 01 January 2025, Published 26 January 2026
Abstract
Let R be a commutative ring with identity. If the nilpotent radical Nil(R) of R is a divided prime ideal, then R is called a \phi-ring. Let R be a \phi-ring and S be a multiplicative subset of R. In this paper, we introduce and study the notions of uniformly nonnil-S-coherent ring, which is “uniform” version of nonnil-S-coherent ring. We give the ideal-theoretic characterizations of uniformly nonnil-S-coherent rings. Besides, we characterize uniformly nonnil-S-coherent rings in terms of \phi-u-S-flat modules and nonnil-u-S-injective modules. Finally, we obtain a strongly uniformly S-versions of the Chase Theorem and Matlis Theorem.
Keywords: nonnil-S-coherent ring, \phi-S-coherent ring, S-coherent ring, nonnil-coherent ring, \phi-S-flat module.
MSC numbers: Primary 13E99, 13A15.
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