Article

Trivial extensions subject to semi-regularity and semi-coherence

Published in: Quaestiones Mathematicae
Volume 43 , issue 1 , 2020 , pages: 45–54

DOI: 10.2989/16073606.2018.1533900

Author(s): K. Adarbeh Department of Mathematics, Palestine , S. Kabbaj Department of Mathematics and Statistics, Saudi Arabia

Keywords: 13C10 , 13C11 , 13E05 , 13F05 , 13H10 , 16A30 , 16A50 , 16A52 , 13C10 , 13C11 , 13E05 , 13F05 , 13H10 , 16A30 , 16A50 , 16A52

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Abstract

In this paper, we investigate the transfer of Matlis’ semi-regularity and semi-coherence in trivial ring extensions issued from rings (with zero-divisors). We use the obtained results to enrich the literature with new examples of semi-regular or semi-coherent rings issued as trivial extensions and validate some questions left open in the literature.

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