Trivial Extensions Defined by Coherent-like Conditions

  title={Trivial Extensions Defined by Coherent-like Conditions},
  author={S. Kabbaj and Najib Mahdou},
  journal={Communications in Algebra},
  pages={3937 - 3953}
Abstract This paper investigates coherent-like conditions and related properties that a trivial extension R ≔ A ∝ E might inherit from the ring A for some classes of modules E. It captures previous results dealing primarily with coherence, and also establishes satisfactory analogues of well-known coherence-like results on pullback constructions. Our results generate new families of examples of rings (with zerodivisors) subject to a given coherent-like condition. 
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THIS is a text–book intended primarily for undergraduates. It is designed to give a broad basis of knowledge comprising such theories and theorems in those parts of algebra which are mentioned in the