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1.
We prove a number of results concerning Armendariz rings and Gaussian rings. Recall that a (commutative) ring R is (Gaussian) Armendariz if for two polynomials f,g∈R[X] (the ideal of R generated by the coefficients of f g is the product of the ideals generated by the coefficients of f and g) fg = 0 implies a i b j=0 for each coefficient a i of f and b j of g. A number of examples of Armendariz rings are given. We show that R Armendariz implies that R[X] is Armendariz and that for R von Neumann regularR is Armendariz if and only if R is reduced. We show that R is Gaussian if and only if each homomorphic image of R is Armendariz. Characterizations of when R[X] and R[X] are Gaussian are given. 相似文献
2.
H. Mousavi 《代数通讯》2013,41(7):3143-3151
In this paper we characterize the finite groups having exactly two conjugacy classes of non-normal subgroups. 相似文献
3.
Ada Peluso 《代数通讯》2013,41(9):3017-3025
ABSTRACT We study conditions on an ideal A of a self-injective R such that the factor ring R/ A is again self-injective, extending certain of our results for PF rings (Faith, 2006). We also consider the same question for p -injective, and for CS -rings. For the CS -rings we consider conditions under which A splits off as a ring direct factor, equivalently, when A is generated by a central idempotent. Definitive results are obtained for an ideal A which is semiprime as a ring, that is, has no nilpotent ideals except zero, and which is a right annihilator ideal. Then A is said to be an r -semiprime right annulet ideal, and is generated by a central idempotent in the following cases: (1) whenever A is generated by an idempotent as a right (or left) ideal (Theorems 3.4, 3.6); (2) in any Baer ring R (Theorem 3.5); (3) in any right and left CS -ring R (Theorem 4.2), and (4) in any right nonsingular right CS -ring R (Theorem 5.5). These results also generalize results of the author in Faith (1985), where it is proven that the maximal regular ideal M( R) splits off in any right and left continuous ring. The results are applied in Section 6 to extend theorems of Faith (1996) characterizing VNR rings, and, as the title of Faith (1996) suggests, extend the conjecture of Shamsuddin. 相似文献
4.
In this article, we investigate when every simple module has a projective (pre)envelope. It is proven that (1) every simple right R-module has a projective preenvelope if and only if the left annihilator of every maximal right ideal of R is finitely generated; (2) every simple right R-module has an epic projective envelope if and only if R is a right PS ring; (3) Every simple right R-module has a monic projective preenvelope if and only if R is a right Kasch ring and the left annihilator of every maximal right ideal of R is finitely generated. 相似文献
5.
Niels Schwartz 《代数通讯》2013,41(11):3796-3814
The real closed valuation rings, i.e., convex subrings of real closed fields, form a proper subclass of the class of real closed domains. It is shown how one can recognize whether a real closed domain is a valuation ring. This leads to a characterization of the totally ordered domains whose real closure is a valuation ring. Real closures of totally ordered factor rings of coordinate rings of real algebraic varieties are very frequently valuation rings. In particular, the real closure of the coordinate ring of a curve is an SV-ring (i.e., the factor rings modulo prime ideals are valuation rings). Real closed valuation rings play a role in the definition of real closed rings, as well as in the construction of real closures of rings and porings. They can also be used for the study of univariate differentiable semi-algebraic functions. This leads to the notion of differentiablility of semi-algebraic functions along half branches of curves. 相似文献
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8.
For a faithful linear representation of a finite group G over a field of characteristic p, we study the ring of invariants. We especially study the polynomial and Cohen–Macaulay properties of the invariant ring. We first show that certain quotient rings of the invariant ring are polynomial rings by which we prove that the Hilbert ideal conjecture is true for a class of groups. In particular, we prove that the conjecture is true for vector invariant rings of Abelian reflection p-groups. Then we study the relationships between the invariant ring of G and that of a subgroup of G. Finally, we study the invariant rings of affine groups and show that, over a finite field, if an affine group contains all translations then the invariant ring is isomorphic to the invariant ring of a linear group. 相似文献
9.
在本文中,严实Hilbert环得到了更进一步的刻划.本文的主要结果是:一个环A是严实Hilbert环,当且仅当多项式环A[X]的每个实极大理想在A上的局限是A的一个极大理想,当且仅当A是实Hilbert环,且A[X]的每个实极大理想是极大的. 相似文献
10.
For a square-free integer d other than 0 and 1, let K = ? ( d ) , where ? is the set of rational numbers. Then K is called a quadratic field and it has degree 2 over ? . For several quadratic fields K = ? ( d ) , the ring Rdof integers of K is not a unique-factorization domain. For d<0, there exist only a finite number of complex quadratic fields, whose ring Rd of integers, called complex quadratic ring, is a unique-factorization domain, i.e., d = −1,−2,−3,−7,−11,−19,−43,−67,−163. Let ϑ denote a prime element of Rd, and let n be an arbitrary positive integer. The unit groups of R d / 〈 v n 〉 was determined by Cross in 1983 for the case d = −1. This paper completely determined the unit groups of R d / 〈 v n 〉 for the cases d = −2,−3. 相似文献
11.
We introduce the so-called multiscale limit for spectral curves associated with real finite-gap sine-Gordon solutions. This
technique allows us to solve the old problem of calculating the density of the topological charge for real finite-gap sine-Gordon
solutions directly from the θ-functional formulae. 相似文献
12.
Yasushi Gomi 《代数通讯》2013,41(1):123-138
The purpose of this paper is to calculate all the character tables of Hecke algebras associated with exceptional Weyl groups and their maximal parabolic subgroups when they are commutative. In the case when Weyl groups are of classical type, they are already known in [D.1] and [D.2]. In §1, we discuss the structure of Hecke algebras and in §2, we calculate all the character tables of these commutative Hecke algebras associated with exceptional Weyl groups. 相似文献
13.
S. Tazhetdinov 《Siberian Mathematical Journal》2008,49(1):175-179
We describe the subnormal subgroups of 2-dimensional linear groups over local and full rings in which 2 is invertible, as well as the subnormal subgroups of symplectic groups over local rings in which 2 is invertible. 相似文献
14.
Sultan Erdoğan Demir 《Topology and its Applications》2012,159(10-11):2580-2591
We compute the monodromy groups of real Enriques surfaces of hyperbolic type. The principal tools are the deformation classification of such surfaces and a modified version of Donaldson?s trick, relating real Enriques surfaces and real rational surfaces. 相似文献
15.
We show that every connected real Lie group can be realized
as the full automorphism group of a Stein hyperbolic
complex manifold. 相似文献
16.
J. Cruickshank 《代数通讯》2019,47(1):101-113
We classify all non-degenerate skew-hermitian forms defined over certain local rings, not necessarily commutative, and study some of the fundamental properties of the associated unitary groups, including their orders when the ring in question is finite. 相似文献
17.
N. Schwartz 《Commentarii Mathematici Helvetici》1997,72(3):434-465
Real closed rings arise in semi-algebraic geometry and topology as well as in the investigation of partially ordered rings.
It is shown that localizations of real closed rings with respect to Gabriel filters, or more generally: multiplicative filters,
are again real closed. Thus, real closedness is preserved under a large number of important ring theoretic constructions.
For a few particularly simple cases the multiplicative filters are classified and the localizations are determined.
Received: August 26, 1996 相似文献
18.
Emilie Dufresne 《Advances in Mathematics》2009,221(6):1979-1989
A separating algebra is, roughly speaking, a subalgebra of the ring of invariants whose elements distinguish between any two orbits that can be distinguished using invariants. In this paper, we introduce a geometric notion of separating algebra. This allows us to prove that only groups generated by reflections may have polynomial separating algebras, and only groups generated by bireflections may have complete intersection separating algebras. 相似文献
19.
S. O. Juriaans I. B. S. Passi Dipendra Prasad 《Proceedings of the American Mathematical Society》2005,133(2):415-423
In this paper we study the groups whose integral group rings have hyperbolic unit groups . We classify completely the torsion subgroups of and the polycyclic-by-finite subgroups of the group . Finally, we classify the groups for which the boundary of has dimension zero.
20.
We consider pairs (K,G) of an infinite field K or a formally real field K and a group G and want to find extension fields
F of K with automorphism group G. If K is formally real then we also want F to be formally real and G must be right orderable.
Besides showing the existence of the desired extension fields F, we are mainly interested in the question about the smallest
possible size of such fields. From some combinatorial tools, like Shelah’s Black Box, we inherit jumps in cardinalities of
K and F respectively. For this reason we apply different methods in constructing fields F: We use a recent theorem on realizations
of group rings as endomorphism rings in the category of free modules with distinguished submodules. Fortunately this theorem
remains valid without cardinal jumps. In our main result (Theorem 1) we will show that for a large class of fields the desired
result holds for extension fields of equal cardinality.
This article was processed by the author using the LATEX style filecljour1 from Springer-Verlag 相似文献