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1.
A. A. Tuganbaev 《Mathematical Notes》1995,58(5):1197-1215
It is proved that a right distributive semiprime PI ringA is a left distributive ring and for each elementx ∈A there is a positive integern such thatx
n
A=Ax
n
. We describe both right distributive right Noetherian rings algebraic over the center of the ring and right distributive
left Noetherian PI rings. We also characterize rings all of whose Pierce stalks are right chain right Artin rings.
Translated fromMatematicheskie Zametki, Vol. 58, No. 5, pp. 736–761, November, 1995. 相似文献
2.
A. A. Tuganbaev 《Journal of Mathematical Sciences》2010,171(2):296-306
A ring A is a completely integrally closed right A-module if and only if the maximal right ring of quotients Q
max(A) of A is an injective right A-module and A is a right completely integrally closed subring in Q
max(A). A right Noetherian, right integrally closed ring A is a completely integrally closed right A-module. 相似文献
3.
G.W.S. Van Rooyen 《代数通讯》2013,41(10):3425-3437
In this paper we show that a ring is a member of the class of rings named in the title if and only if the ring is quasi-reflexive and contains at least one idempotent canonical quasi-ideal.We also prove the latter criterion is equivalent to several other ones.To attain that, we introduce the concept of a left n-socle and dually that of a right n-socle for arbitrary rings.An example is displayed to show that the presence of e.g.a nonzero right n-socle in a ring does not ensure the existence of a nonzero left n-socle.But in the quasi-reflexive case, it turns out that the notion of a left n-socle coincides with the right one.Finally, we give decomposition results which mainly deal with nonzero n-socles of quasi-reflexive rings and their semigroups n-socles concordantly, thereby, generalizing corresponding work in the semiprime case. 相似文献
4.
Let A be a ring, be an injective endomorphism of A, and let
be the right skew polynomial ring. If all right annihilator ideals of A are ideals, then R is a right Bezout ring
is a right Rickartian right Bezout ring, (e)=e for every central idempotent eA, and the element (a) is invertible in A for every regular aA. If A is strongly regular and n 2, then R/x
n
R is a right Bezout ring
R/x
n
R is a right distributive ring
R/x
n
R is a right invariant ring
(e)=e for every central idempotent eA. The ring R/x
2
R is right distributive
R/x
n
R is right distributive for every positive integer n
A is right or left Rickartian and right distributive, (e)=e for every central idempotent eA and the (a) is invertible in A for every regular aA. If A is a ring which is a finitely generated module over its center, then A[x] is a right Bezout ring
A[x]/x
2
A[x] is a right Bezout ring
A is a regular ring. 相似文献
5.
A ringR is said to be a left (right)n-distributive multiplication ring, n>1 a positive integer, if aa1a2...an=aa1aa2...aan (a1a2...ana=a1aa2a...ana) for all a, a1,...,an R. It will be shown that the semi-primitive left (right)n-distributive rings are precisely the generalized boolean ringsA satisfying an=a for all a A. An arbitrary left (right)n-distributive multiplication ring will be seen to be an extension of a nilpotent ringN satisfyingN
n+1=0 by a generalized boolean ring described above. Under certain circumstances it will be shown that this extension splits. 相似文献
6.
D. A. Tuganbaev 《Journal of Mathematical Sciences》2008,149(3):1286-1337
This is a study of ring-theoretic properties of a Laurent ring over a ring A, which is defined to be any ring formed from the additive group of Laurent series in a variable x over A, such that left multiplication by elements of A and right multiplication by powers of x obey the usual rules, and such that the lowest degree of the product of two nonzero series is not less than the sum of the
lowest degrees of the factors. The main examples are skew-Laurent series rings A((x; ϕ)) and formal pseudo-differential operator rings A((t
−1; δ)), with multiplication twisted by either an automorphism ϕ or a derivation δ of the coefficient ring A (in the latter case, take x = t
−1). Generalized Laurent rings are also studied. The ring of fractional n-adic numbers (the localization of the ring of n-adic integers with respect to the multiplicative set generated by n) is an example of a generalized Laurent ring. Necessary and/or sufficient conditions are derived for Laurent rings to be
rings of various standard types. The paper also includes some results on Laurent series rings in several variables.
__________
Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 12, No. 3, pp. 151–224, 2006. 相似文献
7.
A. Mohammadian 《代数通讯》2013,41(12):4568-4574
We show that for any two n × n square-zero matrices A and B over a division ring, if the right column spaces of AB and BA are the same, then the rank of AB is at most n/4, and if, in addition, the right null spaces of AB and BA are the same, then the rank of A + B is at most n/2. This generalizes some known results. 相似文献
8.
A. A. Tuganbaev 《代数通讯》2018,46(4):1716-1721
Every automorphism-invariant non-singular right A-module is injective if and only if the factor ring of the ring A with respect to its right Goldie radical is a right strongly semiprime ring. 相似文献
9.
Let A be a finite-rank, torsion-free, self-small mixed abelian sp-group and let E(A) be the endomorphism ring of A. We give conditions for right and left heredity of E(A). A ring is right hereditary if each of its right ideals is projective. We also find the structure of one-sided ideals of E(A). 相似文献
10.
Let R be a ring, n a fixed nonnegative integer and FP
n
(F
n
) the class of all left (right) R-modules of FP-injective (flat) dimensions at most n. A left R-module M (resp., right R-module F) is called n-FI-injective (resp., n-FI-flat) if Ext
1(N,M) = 0 (resp., Tor
1(F,N) = 0) for any N ∈ FP
n
. It is shown that a left R-module M over any ring R is n-FI-injective if and only if M is a kernel of an FP
n
-precover f: A → B with A injective. For a left coherent ring R, it is proven that a finitely presented right R-module M is n-FI-flat if and only if M is a cokernel of an F
n
-preenvelope K → F of a right R-module K with F projective if and only if M ∈⊥
F
n
. These classes of modules are used to construct cotorsion theories and to characterize the global dimension of a ring. 相似文献
11.
Let A be a local commutative principal ideal ring. We study the double coset space of GL n (A) with respect to the subgroup of upper triangular matrices. Geometrically, these cosets describe the relative position of two full flags of free primitive submodules of A n . We introduce some invariants of the double cosets. If k is the length of the ring, we determine for which of the pairs (n,k) the double coset space depends on the ring in question. For n = 3, we give a complete parametrisation of the double coset space and provide estimates on the rate of growth of the number of double cosets. 相似文献
12.
Let A be a semprime, right noetherian ring equipped with an automorphism α, and let B: = A[[y; α]] denote the corresponding skew power series ring (which is also semiprime and right noetherian). We prove that the Goldie ranks of A and B are equal. We also record applications to induced ideals. 相似文献
13.
An element?σ?of An , the Alternating group of degree n, is extendible in Sn , the Symmetric group of degree n, if there exists a subgroup H of Sn but not An whose intersection with An is the cyclic group generated by σ. A simple number-theoretic criterion, in terms of the cycle-decomposition, for an element of An to be extendible in Sn is given here. 相似文献
14.
A. A. Tuganbaev 《Journal of Mathematical Sciences》2009,156(2):336-341
Let A be a ring that does not contain an infinite set of idempotents that are orthogonal modulo the ideal SI(A
A
). It is proved that all A-modules are I
0-modules if and only if either A is a right semi-Artinian, right V-ring or A/SI(A
A
) is an Artinian serial ring and the square of the Jacobson radical of A/SI(A
A
) isequal to zero.
Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 13, No. 5, pp. 193–200, 2007. 相似文献
15.
Xu Yonghua 《数学学报(英文版)》1990,6(4):323-326
In this paper we shall give a new proof of the well-known theorem of Faith-Utumi[1]. Using our method we can show that every right order ofK
n is a prime right Goldie ring, whereK
n is the n×n-matrix ring over division ring K. Specially,D
n is a prime right Goldie ring, ifD is a right order ofK.The Project Supported by the National Natural Science Foundation of China. 相似文献
16.
A. A. Tuganbaev 《Journal of Mathematical Sciences》2008,149(2):1182-1186
For a large class of rings A, including all rings with right Krull dimension, it is proved that for every automorphism ϕ of the ring A, the Jacobson radical of the skew Laurent series ring A((x, ϕ)) is nilpotent and coincides with N((x, ϕ)), where N is the prime radical of the ring A. If A/N is a ring of bounded index, then the Jacobson radical of the Laurent series ring A((x)) coincides with N((x)).
__________
Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 12, No. 2, pp. 209–215, 2006. 相似文献
17.
Taking the m-power of an entry is a well-defined operation on the unimodular vectors in An modulo addition operations, if n is at least 3, for an arbitrary commutative ring A and any integer m. 相似文献
18.
《Quaestiones Mathematicae》2013,36(3):391-403
Abstract An ideal A of a ring R is called a good ideal if the coset product r 1 r 2 + A of any two cosets r 1 + A and r 2 + A of A in the factor ring R/A equals their set product (r 1 + A) º (r 2 + A): = {(r 1 + a)(r 2 + a 2): a 1, a 2 ε A}. Good ideals were introduced in [3] to give a characterization of regular right duo rings. We characterize the good ideals of blocked triangular matrix rings over commutative principal ideal rings and show that the condition A º A = A is sufficient for A to be a good ideal in this class of matrix rings, none of which are right duo. It is not known whether good ideals in a base ring carries over to good ideals in complete matrix rings over the base ring. Our characterization shows that this phenomenon occurs indeed for complete matrix rings of certain sizes if the base ring is a blocked triangular matrix ring over a commutative principal ideal ring. 相似文献
19.
A ring R is called right Johns if R is right noetherian and every right ideal of R is a right annihilator. R is called strongly right Johns if the matrix ring M n (R) is right Johns for each integer n ≥ 1. The Faith–Menal conjecture is an open conjecture on QF rings. It says that every strongly right Johns ring is QF. It is proved that the conjecture is true if every closed left ideal of the ring R is finitely generated. This result improves the known result that the conjecture is true if R is a left CS ring. 相似文献
20.
Wei Jiaqun 《Czechoslovak Mathematical Journal》2006,56(2):773-780
In this note we show that for a *n-module, in particular, an almost n-tilting module, P over a ring R with A = EndR
P such that P
A
has finite flat dimension, the upper bound of the global dimension of A can be estimated by the global dimension of R and hence generalize the corresponding results in tilting theory and the ones in the theory of *-modules. As an application,
we show that for a finitely generated projective module over a VN regular ring R, the global dimension of its endomorphism ring is not more than the global dimension of R. 相似文献