Computation of Almost Split Sequences with Applications to Relatively Projective and Prinjective Modules

Let be an Artin algebra, let mod be the category of finitely generated -modules, and let Amod be a contravariantly finite and extension closed subcategory. For an indecomposable and not Ext-projective module CA, we compute the almost split sequence 0ABC0 in A from the almost split sequence 0DTrCEC0 in mod. Since the computation is particularly simple if the minimal right A-approximation of DTrC is indecomposable for all indecomposable and not Ext-projective CA, we manufacture subcategories A with the desired property using orthogonal subcategories. The method of orthogonal subcategories is applied to compute almost split sequences for relatively projective and prinjective modules.     

Divisorial Linear Algebra of Normal Semigroup Rings

We investigate the minimal number of generators and the depth of divisorial ideals over normal semigroup rings. Such ideals are defined by the inhomogeneous systems of linear inequalities associated with the support hyperplanes of the semigroup. The main result is that for every bound C there exist, up to isomorphism, only finitely many divisorial ideals I such that (I)C. It follows that there exist only finitely many Cohen–Macaulay divisor classes. Moreover, we determine the minimal depth of all divisorial ideals and the behaviour of and depth in arithmetic progressions in the divisor class group.The results are generalized to more general systems of linear inequalities whose homogeneous versions define the semigroup in a not necessarily irredundant way. The ideals arising this way can also be considered as defined by the nonnegative solutions of an inhomogeneous system of linear diophantine equations.We also give a more ring-theoretic approach to the theorem on minimal number of generators of divisorial ideals: it turns out to be a special instance of a theorem on the growth of multigraded Hilbert functions.     

BRST Resolution for the Principally Graded Wakimoto Module of $$\widehat{\mathfrak{s}\mathfrak{l}}_2 $$

BRST resolution is studied for the principally graded Wakimoto module of recently found in math.QA/0005203. The submodule structure is completely determined and irreducible representations can be obtained as the zero-th cohomology group.     

Finitely Valued f-Modules, An Addendum

In an -group M with an appropriate operator set it is shown that the -value set (M) can be embedded in the value set (M). This embedding is an isomorphism if and only if each convex -subgroup is an -subgroup. If (M) has a.c.c. and M is either representable or finitely valued, then the two value sets are identical. More generally, these results hold for two related operator sets ₁ and ₂ and the corresponding -value sets and . If R is a unital -ring, then each unital -module over R is an f-module and has exactly when R is an f-ring in which 1 is a strong order unit.     

A Five-term Exact Sequence for Opext of Crossed Modules in Lie Algebras

Extensions of crossed modules in Lie algebras with abelian kernel are studied, particularly backward and forward induced extensions and related properties. The set Opext((U, Q, ), (R, K, )) of congruence classes of extensions of (R, K, ) by (U, Q, ) is endowed with a K-vector space structure. This K-vector space appears in a five-term natural and exact sequence associated with an extension of crossed modules.2000 Mathematics Subject Classification: 17B56, 17B99, 18G99     

Product-trace-rings and a question of G. S. Garfinkel

It is an open question as to whether every left coherent ring satisfying the intersection property for finitely generated left ideals of is a right-product-trace-ring or not. is a right-product-trace-ring iff every product of trace-right--modules (= universally torsionless-right--modules) is a trace-right--module. This question is shown to have a negative answer. Furthermore, looking at all valuation domains, the complete product-trace-rings, the product-trace-rings and the product-content-rings are characterized.

     

Finite groups of matrices over group rings

We investigate certain finite subgroups of , where is a finite nilpotent group. Such a group gives rise to a -module; we study the characters of these modules to limit the structure of . We also exhibit some exotic subgroups .

     

ICF靶用空心玻璃微球耐压性能测试

 利用自行研制的空心微球耐外压装置和充气装置，测试了目前激光惯性约束聚变实验打靶使用的空心玻璃微球耐内压能力和耐外压能力。空心玻璃微球采用液滴法制备，直径为180～250 mm、壁厚为0.8~4.0 mm。理论计算表明，当微球纵横比超过90时，耐外压能力与球壳材料的杨氏模量有关，由此测量得到的空心玻璃微球杨氏模量为55~75 GPa。玻璃微球的耐内压能力主要与球壳材料的抗拉强度有关，实验测量得到的玻璃微球抗拉强度为90~140 MPa。     

Extending modules relative to a torsion theory

An R-module M is said to be an extending module if every closed submodule of M is a direct summand. In this paper we introduce and investigate the concept of a type 2 τ-extending module, where τ is a hereditary torsion theory on Mod-R. An R-module M is called type 2 τ-extending if every type 2 τ-closed submodule of M is a direct summand of M. If τ _I is the torsion theory on Mod-R corresponding to an idempotent ideal I of R and M is a type 2 τ _I -extending R-module, then the question of whether or not M/MI is an extending R/I-module is investigated. In particular, for the Goldie torsion theory τ _G we give an example of a module that is type 2 τ _G -extending but not extending.     

JavaStatSoft: design patterns and features

JavaStatSoft, implemented using Java, is an open-source software for performing statistics. The current features of JavaStatSoft are described. Several well-known patterns the software used are introduced. In addition, based on these patterns and the experience in developing the software, a new framework, referred to as Data Analysis Module, is proposed to help programmers develop a user-friendly software for data analysis.