Atomic semigroup rings and the ascending chain condition on principal ideals

An integral domain is called atomic if every nonzero nonunit element factors into irreducibles. On the other hand, an said to satisfy ascending chain condition on principal ideals (ACCP) of stabilizes. It was asserted by P. Cohn back in sixties that satisfies ACCP, but such assertion refuted A. Grams seventies with a neat counterexample. Still, domains without ACCP are notoriously elusive, and just few classes have been found since Grams’ first construction. In part this paper, we generalize construction provide new ACCP. second construct class semigroup rings