If A is a commutative ring with identity and B is a unitary A-algebra, B is locally polynomial
over A provided that for every prime p of A, ${B_p}= B {\otimes _A}{A_p} $ is a polynomial …

Let D be an integral domain, and let A be a domain containing D with quotient field K. We
will say that the extension A of D is polynomially complete if D is a polynomially dense …

Let $ R $ be a commutative ring with identity, let $ X $ be an indeterminate, and let $ I $ be
an ideal of the polynomial ring $ R [X] $. Let $\min I $ denote the set of elements of $ I $ of …

Let R be an associative ring and denote by the injective hull of the right module RR. If can be
endowed with a ring multiplication which extends the existing module multiplication, we say …

Let R be a commutative ring. We say that R satisfies the ascending chain condition for
principal ideals, or that R has property (M), if each ascending sequence (a1)⊆(a2)⊆… of …

MODULES OVER SEMIHEREDITARY BEZOUT RINGS Page 1 PROCEEDINGS OF THE
AMERICAN MATHEMATICAL SOCIETY Volume 46, Number 2, November 1974 MODULES …

ANY finitely generated Abelian group A is a finite direct sum of cyclic groups. Gathering
together the infinite cyclic direct summands in this decomposition of A it follows that A= B© …

JP Serre raised in [6] the following question:(S) Is the polynomial ring K [X1, X2,•••, Xn] with a
finite number of variables X1, X2,•••, Xn over a field K a PF domain? It is well-known (cf.[3]) …

1. Introduction. If A is an integral domain and S is a subset of A not containing zero, then one
can form the quotient ring As which lies between A and its quotient field. It is well known that …

Let $ D $ and $ J $ be integral domains such that $ D\subset J $ and $ J [[X]] $ is not
algebraic over $ D [[X]] $. Is it necessarily the case that there exists an integral domain $ R …