this work is a continuation of [a‎. ‎o‎. ‎asar‎, ‎‎‎on infinitely generated groups whose proper subgroups are solvable‎, ‎{em j‎. ‎algebra}‎, ‎{bf 399} (2014) 870-886.]‎, ‎where it was shown‎ ‎that a perfect infinitely generated group whose proper subgroups‎ are solvable and in whose homomorphic images normal closures of ‎finitely generated subgroups are residually nilpotent is a fitting‎‎$p$-g...

We study finitely generated models of countable theories, having at most countably many nonisomorphic finitely generated models. We introduce a notion of rank of finitely generated models and we prove, when T has at most countably many nonisomorphic finitely generated models, that every finitely generated model has an ordinal rank. This rank is used to give a property of finitely generated mode...

We prove the following. Let R be a Noetherian commutative ring, B a finitely generated R-algebra, and A a pure R-subalgebra of B. Then A is finitely generated over R. In this paper, all rings are commutative. Let A be a ring and B an A-algebra. We say that A → B is pure, or A is a pure subring of B, if for any A-module M , the map M = M ⊗A A → M ⊗A B is injective. Considering the case M = A/I, ...