Semigroup rings which are finite direct products of Galois rings
Let \(R\) be an associative ring, and let \(p\) be a prime. A polynomial \(f\in R[x]\) is said to be irreducible modulo \(p\) if so is the image of \(f\) under the natural ring homomorphism \(R[x]\to R[x]/pR[x]\). A Galois ring is a ring of the form \((\mathbb{Z}/p^m\mathbb{Z})[x]/(f(x))\), where \(p\) is a prime, and \(f(x)\in(\mathbb{Z}/p^m\mathbb{Z})[x]\) is a monic polynomial that is irreducible modulo \(p\). The author gives a full description of the commutative semigroup rings in the title.
scientific article; zbMATH DE number 1356250