Rings admitting nonzero homomorphisms between non-injective modules
N Er, Z Türkoğlu - Communications in Algebra, 2018 - Taylor & Francis
Communications in Algebra, 2018•Taylor & Francis
ABSTRACT A variety of rings including those that are Morita equivalent to local perfect rings,
two by two upper triangular matrix rings over a division ring or certain rings arising in the
framework of rings described by various test modules for injectivity satisfy a common
property: there is a nonzero homomorphism between any two non-injective modules. In this
paper, after settling a special case inspired by a concept due to Enochs as the first step, we
provide a complete characterization of the rings of the title.
two by two upper triangular matrix rings over a division ring or certain rings arising in the
framework of rings described by various test modules for injectivity satisfy a common
property: there is a nonzero homomorphism between any two non-injective modules. In this
paper, after settling a special case inspired by a concept due to Enochs as the first step, we
provide a complete characterization of the rings of the title.
Abstract
A variety of rings including those that are Morita equivalent to local perfect rings, two by two upper triangular matrix rings over a division ring or certain rings arising in the framework of rings described by various test modules for injectivity satisfy a common property: there is a nonzero homomorphism between any two non-injective modules. In this paper, after settling a special case inspired by a concept due to Enochs as the first step, we provide a complete characterization of the rings of the title.
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