SIFAT-SIFAT ALJABAR AMALGAMASI SEPANJANG IDEAL DAN APLIKASINYA - Utami, Rintang; Wahyuni, Sri (University of Mataram, 2025)
If given rings A and B, a ring homomorphism f : A –> B, and an ideal J of B, then a new ring can be constructed called amalgamated algebras along an ideal which is denoted by A ^f J := (a, f(a)+j) a A, j J with component-wise addition and multiplication. This paper discusses the construction, definition, properties such as isomporhisms, and characterization of amalgamated algebras along an ideal that is a prime ring and a Noetherian ring with detailed explanations. We also discuss its characterization as a reduced ring, which is a continuation from the previous paper. Furthermore, we investigate its characterization as an Artinian ring by adding an additional condition that every ideal of J has unity.