Almost factoriality of integral domains and Krull-like domains
نویسندگان
چکیده
منابع مشابه
Semistar dimension of polynomial rings and Prufer-like domains
Let $D$ be an integral domain and $star$ a semistar operation stable and of finite type on it. We define the semistar dimension (inequality) formula and discover their relations with $star$-universally catenarian domains and $star$-stably strong S-domains. As an application, we give new characterizations of $star$-quasi-Pr"{u}fer domains and UM$t$ domains in terms of dimension inequal...
متن کاملOn Gröbner bases and Krull dimension of residue class rings of polynomial rings over integral domains
Given an ideal a in A[x1, . . . , xn] where A is a Noetherian integral domain, we propose an approach to compute the Krull dimension of A[x1, . . . , xn]/a, when the residue class ring is a free A-module. When A is a field, the Krull dimension of A[x1, . . . , xn]/a has several equivalent algorithmic definitions by which it can be computed. But this is not true in the case of arbitrary Noetheri...
متن کاملPower Series over Generalized Krull Domains
We resolve an open problem in commutative algebra and Field Arithmetic, posed by Jarden – Let R be a generalized Krull domain. Is the ring R[[X]] of formal power series over R a generalized Krull domain? We show that the answer is negative.
متن کاملsemistar dimension of polynomial rings and prufer-like domains
let $d$ be an integral domain and $star$ a semistar operation stable and of finite type on it. we define the semistar dimension (inequality) formula and discover their relations with $star$-universally catenarian domains and $star$-stably strong s-domains. as an application, we give new characterizations of $star$-quasi-pr"{u}fer domains and um$t$ domains in terms of dimension ine...
متن کاملAlmost Condensed Domains
As an extension of the class of half condensed domains introduced by D.D. Anderson and Dumitrescu, we introduce and study the class of almost condensed domains. An integral domain D is almost condensed if whenever 0 ̸= z ∈ IJ with I, J ideals of D, there exist I ′, J ′ ideals of D such that I ′ ⊆ Iw, J ′ ⊆ Jw and zD = (I ′J )w. In 1983, D.F. Anderson and D.E. Dobbs [13] called an integral domain...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 2012
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.2012.260.129