On graded coherent-like properties in trivial ring extensions - KOÇ, SUAT; TEKİR, ÜNSAL (SPRINGER INT PUBL AG, 2022)
Let A = circle plus(alpha is an element of G) A(alpha) be a commutative ring with unity graded by an arbitrary grading commutative monoid G, E be a graded A-module and R = A proportional to E the graded trivial extension. In this paper, in the second section, we improve some results on graded trivial extension and we give some new ones and the theme throughout is how homogeneous properties are related to those of A and E. Then, in another section, we introduce and study the notions of graded-v-coherent, graded-quasi-coherent and graded-finite conductor rings, then we study their transfer in the graded trivial extension.
Keywords: Graded trivial extension; Trivial extension; Graded modules and rings; Coherent rings and modules; Graded-v-coherence; MODULES