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991.
Behrouz Edalatzadeh 《代数通讯》2013,41(8):3366-3380
In this paper, we introduce the concept of capability for crossed modules of Lie algebras, which is a generalization of capability in Lie algebras and groups. By using a special central ideal of a crossed module, we give a sufficient condition for the capability of a crossed module of Lie algebras. Also, we will extend the five-term exact sequence on homology of crossed modules of Lie algebras one term further and study the connection between the capability of crossed modules and this sequence. Finally, we study the relation between the capability and the center of a cover of a crossed module. 相似文献
992.
A right module M over a ring R is said to be ADS if for every decomposition M = S ⊕ T and every complement T′ of S, we have M = S ⊕ T′. In this article, we study and provide several new characterizations of this new class of modules. We prove that M is semisimple if and only if every module in σ[M] is ADS. SC and SI rings also characterized by the ADS notion. A ring R is right SC-ring if and only if every 2-generated singular R-module is ADS. 相似文献
993.
For an extension E: R ? S of (commutative) rings and the induced extension F: R(X) ? S(X) of Nagata rings, the transfer of the FCP and FIP properties between E and F is studied. Then F has FCP ? E has FCP. The extensions E for which F has FIP are characterized. While E has FIP whenever F has FIP, the converse fails for certain subintegral extensions; it does hold if E is integrally closed, seminormal, or subintegral with R quasi-local having infinite residue field. If F has FIP, conditions are given for the sets of intermediate rings of E and F to be order-isomorphic. 相似文献
994.
Positivity in *-algebras can be defined either algebraically, by quadratic modules, or analytically, by *-representations. By the induction procedure for *-representations, we can lift the analytical notion of positivity from a *-subalgebra to the entire *-algebra. The aim in this article is to define and study the induction procedure for quadratic modules. The main question is when a given quadratic module on the *-algebra is induced from its intersection with the *-subalgebra. This question is very hard even for the smallest quadratic module (i.e. the set of all sums of hermitian squares) and will be answered only in very special cases. 相似文献
995.
François Couchot 《代数通讯》2013,41(1):381-389
It is proven that the weak dimension of each FP-injective module over a chain ring which is either Archimedean or not semicoherent is less or equal to 2. This implies that the projective dimension of any countably generated FP-injective module over an Archimedean chain ring is less or equal to 3. 相似文献
996.
Bart de Bruyn 《Linear and Multilinear Algebra》2013,61(7):887-902
Let V be 2n-dimensional vector space over a field 𝕂 equipped with a nondegenerate skew-ψ-Hermitian form f of Witt index n ≥ 1, let 𝕂0 ? 𝕂 be the fix field of ψ and let G denote the group of isometries of (V, f). For every k ∈ {1, …, 2n}, there exist natural representations of the groups G ? U(2n, 𝕂/𝕂0) and H = G ∩ SL(V) ? SU(2n, 𝕂/𝕂0) on the k-th exterior power of V. With the aid of linear algebra, we prove some properties of these representations. We also discuss some applications to projective embeddings and hyperplanes of Hermitian dual polar spaces. 相似文献
997.
N. Dehghani 《代数通讯》2013,41(11):4732-4748
For certain classes 𝒞 of R-modules, including singular modules or modules with locally Krull dimensions, it is investigated when every module in 𝒞 with a finitely generated essential submodule is finitely generated. In case 𝒞 = Mod-R, this means E(M)/M is Noetherian for any finitely generated module MR. Rings R with latter property are studied and shown that they form a class 𝒬 properly between the class of pure semisimple rings and the class of certain max rings. Duo rings in 𝒬 are precisely Artinian rings. If R is a quasi continuous ring in 𝒬 then R ? A ⊕ T where A is a semisimple Artinian ring and T ∈ 𝒬 with Z(TT) ≤ess TT. 相似文献
998.
999.
William C. Brown 《代数通讯》2013,41(12):6051-6067
Suppose R is an integral domain and A ∈ M n × n(R) \{O}. If D is a spanning rank partner of A, then precisely one of the following three relationships holds: N A = N D N A = XN D or XN A = N D. Here X is an indeterminate and N A(N D) denotes the null ideal of A(D) in R[X]. There are easy examples of A and D for which N A = N D and N A = XN D. In this paper, we give an example where XN A = N D. We give sharper versions of the theorem for n ≤ 4. 相似文献
1000.
Let R be a commutative Noetherian ring, K a nonzero finitely generated suitable R-module, and I an ideal of R. It is shown that if (R, ) is local, then is G K -perfect if and only if K is a canonical module for R. Furthermore, if I is integrally closed and G K ? dim R I < ∞, then K is a canonical R -module for every ? Ass R R/I whenever K satisfies Serre's condition (S 1) or grade K I > 0. Finally, it is shown that if CM ? dim R I < ∞, then R is Cohen–Macaulay for every ? Ass R R/I. 相似文献