Integral domains having a unique Kronecker function ring
نویسندگان
چکیده
منابع مشابه
Unique Factorization in Integral Domains
Throughout R is an integral domain unless otherwise specified. Let A and B be sets. We use the notation A ⊆ B to indicate that A is a subset of B and we use the notation A ⊂ B to mean that A is a proper subset of B. The group of elements in R which have a multiplicative inverse (the group of units of R) is denoted R×. Since R has no zero divisors cancellation holds. If a, b, c ∈ R and a 6= 0 th...
متن کاملIntegral Domains Having Nonzero Elements with Infinitely Many Prime Divisors
In a factorial domain every nonzero element has only finitely many prime divisors. We study integral domains having nonzero elements with infinitely many prime divisors. Let D be an integral domain. It is well known that if D is a UFD then every nonzero element has only finitely many prime divisors (see e.g. [G]). This is also true if D is a Noetherian domain, or more generally, if D satisfies ...
متن کاملLocally GCD domains and the ring $D+XD_S[X]$
An integral domain $D$ is called a emph{locally GCD domain} if $D_{M}$ is aGCD domain for every maximal ideal $M$ of $D$. We study somering-theoretic properties of locally GCD domains. E.g., we show that $%D$ is a locally GCD domain if and only if $aDcap bD$ is locally principalfor all $0neq a,bin D$, and flat overrings of a locally GCD domain arelocally GCD. We also show that the t-class group...
متن کاملIs Having a Unique Equilibrium Robust?
We investigate whether having a unique equilibrium (or a given number of equilibria) is robust to perturbation of the payoffs, both for Nash equilibrium and correlated equilibrium. We show that the set of n-player finite games with a unique correlated equilibrium is open, while this is not true of Nash equilibrium for n > 2. The crucial lemma is that a unique correlated equilibrium is a quasi-s...
متن کاملA Course on Integral Domains
My son who is in the 4 grade is learning about prime numbers and cancelling prime numbers in order to reduce fractions into lowest forms. I have told him that every number (positive integer) can be expressed as a product of primes, and surely along the road, his teachers will confirm this. We will consider this property in integral domains. We say that a divides b in the domain R, and write a |...
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: Journal of Pure and Applied Algebra
سال: 2011
ISSN: 0022-4049
DOI: 10.1016/j.jpaa.2010.07.012