相关论文: Universally catenarian integral domains, strong S-…

This note investigates two long-standing conjectures on the Krull dimension of integer-valued polynomial rings and of polynomial rings, respectively, in the context of (locally) essential domains.

In 1994, Matsuda and Okabe introduced the notion of semistar operation, extending the "classical" concept of star operation. In this paper, we introduce and study the notions of semistar linkedness and semistar flatness which are natural…

Let $\ast$ be a star operation on an integral domain $D$. Let $\f(D)$ be the set of all nonzero finitely generated fractional ideals of $D$. Call $D$ a $\ast$--Pr\"ufer (respectively, $(\ast, v)$--Pr\"ufer) domain if $(FF^{-1})^{\ast}=D$…

We consider properties and applications of a new topology, called the Zariski topology, on the space ${\rm SStar}(A)$ of all the semistar operations on an integral domain $A$. We prove that the set of all overrings of $A$, endowed with the…

We introduce a new class of integral domains, the perinormal domains, which fall strictly between Krull domains and weakly normal domains. We establish basic properties of the class, and in the case of universally catenary domains we give…

Let $R$ be a real closed field and let ${\mathcal S}(M)$ be the ring of (continuous) semialgebraic functions on a semialgebraic set $M\subset R^n$ and let ${\mathcal S}^*(M)$ be its subring of bounded semialgebraic functions. In this work…

Given a star operation * of finite type, we call a domain R a *-unique representation domain (*-URD) if each *-invertible *-ideal of R can be uniquely expressed as a *-product of pairwise *-comaximal ideals with prime radical. When * is the…

Let $D$ be an integral domain with quotient field $K$. The $b$-operation that associates to each nonzero $D$-submodule $E$ of $K$, $E^b := \bigcap\{EV \mid V valuation overring of D\}$, is a semistar operation that plays an important role…

Let $\ast $ be a finite character star operation defined on an integral domain $D.$ Call a nonzero $\ast $-ideal $I$ of finite type a $\ast $ -homogeneous ($\ast $-homog) ideal, if $I\subsetneq D$ and $(J+K)^{\ast }\neq D$ for every pair…

Let $D$ be a principal ideal domain with infinite spectrum such that for every nonzero prime ideal $M$ of $D$, the residue field $D/M$ is finite. Let $K$ be the quotient field of $D$. We investigate sets of lengths in the ring of…

Let $\star$ be a semistar operation on a domain $D$, $\star_f$ the finite-type semistar operation associated to $\star$, and $D$ a Pr\"ufer $\star$-multiplication domain (P$\star$MD). For the special case of a Pr\"ufer domain (where $\star$…

Let $R$ be an integral domain, $Star(R)$ the set of all star operations on $R$ and $StarFC(R)$ the set of all star operations of finite type on $R$. Then $R$ is said to be star regular if $|Star(T)|\leq |Star(R)|$ for every overring $T$ of…

Let $D$ be an integral domain with quotient field $K$. Call an overring $S$ of $D$ a subring of $K$ containing $D$ as a subring. A family $\{S_\lambda\mid\lambda \in \Lambda \}$ of overrings of $D$ is called a defining family of $D$, if $D…

This paper seeks ring-theoretic conditions of an integral domain R that reflect in the Clifford property or Boolean property of its class semigroup S(R), that is, the semigroup of the isomorphy classes of the nonzero (integral) ideals of R…

Recently, N. Epstein and J. Shapiro introduced and studied the perinormal domains: those domains A whose going down overrings are flat A-modules. We show that every Pr\"ufer v-multiplication domain is perinormal and has no proper lying over…

A semidomain is an additive submonoid of an integral domain that is closed under multiplication and contains the identity element. Although atomicity and divisibility in integral domains have been systematically investigated for more than…

Let $S$ be an integral domain with field of fractions $F$ and let $A$ be an $F$-algebra having an $S$-stable basis. We prove the existence of an $S$-subalgebra $R$ of $A$ lying over $S$ whose localization with respect to $S$ is $A$ (we call…

Let $A\subset B$ be an integral ring extension of integral domains with fields of fractions $K$ and $L$, respectively. The integral degree of $A\subset B$, denoted by ${\rm d}_A(B)$, is defined as the supremum of the degrees of minimal…

The paper studies some properties of the ring of integer-valued quasi-polynomials. On this ring, theory of generalized Euclidean division and generalized GCD are presented. Applications to finite simple continued fraction expansion and…

We study domain wall solutions in d=5, N=2 supergravity coupled to a single hypermultiplet whose moduli space is described by certain inhomogeneous, toric ESD manifolds constructed recently by Calderbank and Singer. Upon gauging a generic…