منابع مشابه
Gersten’s conjecture for commutative discrete valuation rings
The purpose of this article is to prove that Gersten’s conjecture for a commutative discrete valuation ring is true. Combining with the result of [GL87], we learn that Gersten’s conjecture is true if the ring is a commutative regular local, smooth over a commutative discrete valuation ring.
متن کاملON COMMUTATIVE GELFAND RINGS
A ring is called a Gelfand ring (pm ring ) if each prime ideal is contained in a unique maximal ideal. For a Gelfand ring R with Jacobson radical zero, we show that the following are equivalent: (1) R is Artinian; (2) R is Noetherian; (3) R has a finite Goldie dimension; (4) Every maximal ideal is generated by an idempotent; (5) Max (R) is finite. We also give the following resu1ts:an ideal...
متن کاملOn Commutative Reduced Baer Rings
It is shown that a commutative reduced ring R is a Baer ring if and only if it is a CS-ring; if and only if every dense subset of Spec (R) containing Max (R) is an extremally disconnected space; if and only if every non-zero ideal of R is essential in a principal ideal generated by an idempotent.
متن کاملNon-commutative reduction rings
Reduction relations are means to express congruences on rings. In the special case of congruences induced by ideals in commutative polynomial rings, the powerful tool of Gröbner bases can be characterized by properties of reduction relations associated with ideal bases. Hence, reduction rings can be seen as rings with reduction relations associated to subsets of the ring such that every finitel...
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 1992
ISSN: 0022-247X
DOI: 10.1016/0022-247x(92)90364-j