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1.
Let a be a regular element of a ring R. If either K:=r R (a) has the exchange property or every power of a is regular, then we prove that for every positive integer n there exist decompositionswhere \(Y_{n} \subseteq a^{n}R\) and E n ?R/a R. As applications we get easier proofs of the results that a strongly π-regular ring has stable range one and also that a strongly π-regular element whose every power is regular is unit-regular.
相似文献
$$R_{R} = K \oplus X_{n} \oplus Y_{n} = E_{n} \oplus X_{n} \oplus aY_{n}, $$
2.
We unify the cancellation property of rings with stable range one and the principal ideal domain by introducing a new notion
which is called “cancellable range”. It is proved that if a ring R has cancellable range n for some positive integer n, then for any n-generated module B and any module
implies B ≅ C; if R is a Noetherian ring and R has cancellable range n for any n ≧ 1, then R has the cancellation property.
Received: 16 November 2004 相似文献
3.
Let R be a ring and M a right R-module. M is called -cofinitely supplemented if every submodule N of M with M/N finitely generated has a supplement that is a direct summand of M. In this paper various properties of the -cofinitely supplemented modules are given. It is shown that (1) Arbitrary direct sum of -cofinitely supplemented modules is -cofinitely supplemented. (2) A ring R is semiperfect if and only if every free R-module is -cofinitely supplemented. In addition, if M has the summand sum property, then M is -cofinitely supplemented iff every maximal submodule has a supplement that is a direct summand of M. 相似文献
4.
Carlo Mariconda 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(4):828-801
Let w∗(x)=a⋅x+b be an affine function in RN, Ω⊂RN, L:RN→R be convex and w be a local minimizer of
5.
Let \((R,\mathfrak {m})\) be a Noetherian local ring, I be an ideal of R, and M be a finitely generated R-module such that \({\text {H}}_I^t(M)\) is Artinian and I-cofinite, where \(t={\text {cd}}\,(I,M)\). In this paper, we give some equivalent conditions for the property Also, we show that if \({\text {H}}_I^t(M)\) satisfies the property \((*)\), then \({\text {H}}_I^t(M)\cong {\text {H}}_{\mathfrak {m}}^t(M/N)\) for some submodule N of M with \({\text {dim}}\,(M/N)=t\).
相似文献
$$\begin{aligned} {\text {Ann}}\,_R\left( 0:_{{\text {H}}_I^t (M)} \mathfrak {p}\right) =\mathfrak {p}~\text {for all prime ideals }~ \mathfrak {p}\supseteq {\text {Ann}}\,_R{\text {H}}_I^t(M).(*) \end{aligned}$$
6.
Lior Fishman 《Journal of Number Theory》2009,129(9):2133-2153
We prove that for every M,N∈N, if τ is a Borel, finite, absolutely friendly measure supported on a compact subset K of RMN, then K∩BA(M,N) is a winning set in Schmidt's game sense played on K, where BA(M,N) is the set of badly approximable M×N matrices. As an immediate consequence we have the following application. If K is the attractor of an irreducible finite family of contracting similarity maps of RMN satisfying the open set condition (the Cantor's ternary set, Koch's curve and Sierpinski's gasket to name a few known examples), then
dimK=dimK∩BA(M,N). 相似文献
7.
Hoai-Minh Nguyen 《Journal of Functional Analysis》2006,237(2):689-720
In this paper, we present some new characterizations of Sobolev spaces. Here is a typical result. Let g∈Lp(RN), 1<p<+∞; we prove that g∈W1,p(RN) if and only if
8.
Given a bounded domain Ω in RN, and a function a∈Lq(Ω) with q>N/2, we study the existence of a positive solution for the quasilinear problem
9.
Anand P. Singh 《Journal of Mathematical Analysis and Applications》2007,335(2):907-914
Let L be the set of all entire functions f such that for given ?>0,
logL(r,f)>(1−?)logM(r,f) 相似文献
10.
Jordan maps on triangular algebras 总被引:1,自引:0,他引:1
Ji Peisheng 《Linear algebra and its applications》2007,426(1):190-198
Let T be a triangular algebra and R′ be an arbitrary ring. Suppose that M:T→R′ and M∗:R′→T are surjective maps such that
11.
Zhanmin Zhu 《Czechoslovak Mathematical Journal》2018,68(2):455-474
Let R be a ring. A subclass T of left R-modules is called a weak torsion class if it is closed under homomorphic images and extensions. Let T be a weak torsion class of left R-modules and n a positive integer. Then a left R-module M is called T-finitely generated if there exists a finitely generated submodule N such that M/N ∈ T; a left R-module A is called (T,n)-presented if there exists an exact sequence of left R-modules such that F0,..., Fn?1 are finitely generated free and Kn?1 is T-finitely generated; a left R-module M is called (T,n)-injective, if Ext n R (A,M) = 0 for each (T, n+1)-presented left R-module A; a right R-module M is called (T,n)-flat, if Tor R n (M,A) = 0 for each (T, n+1)-presented left R-module A. A ring R is called (T,n)-coherent, if every (T, n+1)-presented module is (n + 1)-presented. Some characterizations and properties of these modules and rings are given.
相似文献
$$0 \to {K_{n - 1}} \to {F_{n - 1}} \to \cdots \to {F_1} \to {F_0} \to M \to 0$$
12.
Let W and M be two finite dimensional subspaces of a Hilbert space H such that H=W⊕M⊥, and let PW‖M⊥ denote the oblique projection with range W and nullspace M⊥. In this article we get the following formula for the singular values of PW‖M⊥
13.
Qingyi Zeng 《Czechoslovak Mathematical Journal》2015,65(4):891-904
An S-closed submodule of a module M is a submodule N for which M/N is nonsingular. A module M is called a generalized CS-module (or briefly, GCS-module) if any S-closed submodule N of M is a direct summand of M. Any homomorphic image of a GCS-module is also a GCS-module. Any direct sum of a singular (uniform) module and a semi-simple module is a GCS-module. All nonsingular right R-modules are projective if and only if all right R-modules are GCS-modules. 相似文献
14.
In the present paper we deal with the polynomials Ln(α,M,N) (x) orthogonal with respect to the Sobolev inner product
15.
Let hR denote an L∞ normalized Haar function adapted to a dyadic rectangle R⊂d[0,1]. We show that for choices of coefficients α(R), we have the following lower bound on the L∞ norms of the sums of such functions, where the sum is over rectangles of a fixed volume:
16.
Li Liang 《Algebras and Representation Theory》2013,16(6):1541-1560
We introduce and investigate Tate homology $\widehat{{\mbox{\rm tor}}}$ of modules of finite Gorenstein flat dimension. In particular, we show that over a right coherent ring R, $\widehat{{\mbox{\rm tor}}}_{i}^{R}(M,N)\cong\widehat{{\mbox{\rm Tor}}}_{i}^{R}(M,N)$ for any right R-module M of finite Gorenstein projective dimension, any R-module N of finite Gorenstein flat dimension and any i?∈??. We also study the Tate homology $\widehat{{\mbox{\rm tor}}}$ of a cotorsion module of finite Gorenstein flat dimension in the paper. 相似文献
17.
Zhaoxia Liu 《Journal of Mathematical Analysis and Applications》2011,382(2):731-747
In this paper, we consider the elliptic system of two equations in H1(RN)×H1(RN):
18.
19.
When A∈B(H) and B∈B(K) are given, we denote by MC the operator acting on the infinite dimensional separable Hilbert space H⊕K of the form . In this paper, it is shown that a 2×2 operator matrix MC is upper semi-Fredholm and ind(MC)?0 for some C∈B(K,H) if and only if A is upper semi-Fredholm and
20.
Let L be a Schrdinger operator of the form L =-? + V acting on L~2(R~n), n≥3, where the nonnegative potential V belongs to the reverse Hlder class B_q for some q≥n. Let BMO_L(R~n) denote the BMO space associated to the Schrdinger operator L on R~n. In this article, we show that for every f ∈ BMO_L(R~n) with compact support, then there exist g ∈ L~∞(R~n) and a finite Carleson measure μ such that f(x) = g(x) + S_(μ,P)(x) with ∥g∥∞ + |||μ|||c≤ C∥f∥BMO_L(R~n), where S_(μ,P)=∫(R_+~(n+1))Pt(x,y)dμ(y, t),and Pt(x, y) is the kernel of the Poisson semigroup {e-~(t(L)~(1/2))}t0 on L~2(R~n). Conversely, if μ is a Carleson measure, then S_(μ,P) belongs to the space BMO_L(R~n). This extends the result for the classical John-Nirenberg BMO space by Carleson(1976)(see also Garnett and Jones(1982), Uchiyama(1980) and Wilson(1988)) to the BMO setting associated to Schrdinger operators. 相似文献