Natural Classes,Left Exact Preradicals,and Flat Epimorphisms

We define a function between the lattice of left exact preradicals in R-mod and the complete boolean lattice R-nat of natural classes in R-mod in such a way that the image of this function results to be a complete sublattice of R-nat. The image of this function is R-nat if and only if R is left semiartinian. We prove that every flat ring epimorphism from R to S induces a function between the lattice of left exact preradicals in R-mod and the lattice of left exact preradicals in S-mod. In this context, we obtain a lattice decomposition of S-nat for each left exact preradical.     

实时三维超声心动图与640层CT定量评价冠心病患者左心室容积及收缩功能的对比研究

目的应用实时三维超声心动图（RT-3DE）和640层CT（640- MSCT）定量评价左心室容积和收缩功能,探讨两种方法测值的相关性及在左心功能评价中的应用价值。方法选择临床或冠状动脉造影确诊为冠心病的患者42例,分别行RT-3DE和640- MSCT心脏增强（分别采用自动法和手动法）检查,测量指标包括：左心室舒张末期容积（LVEDV）、左心室收缩末期容积（LVESV）、左心室每搏输出量（LVSV）和左心室射血分数（LVEF）。将两种方法各测量值的结果进行比较。结果（1）RT-3DE测得左心容积及功能指标与640- MSCT （自动、手动两种方法）测值（LVEDV、LVESV、LVSV及LVEF）间相关性较好（P＜0.01）;（2）640- MSCT与RT-3DE左心室容积与心功能测值之间差别在于：LVEDV、LVESV两项指标640- MSCT测值均高于RT-3DE测值（P＜0.05）,LVSV值640- MSCT测值稍高于RT-3DE测值（P＞0.05）,而LVEF值640- MSCT测值稍低于RT-3DE测值（P＞0.05）。结论640- MSCT与RT-3DE在评价冠心病患者左心容积及功能方面高度相关,RT-3DE可推荐为临床首选影像学检查;根据不同患者的病情和各自特点,将640- MSCT与RT-3DE结合使用,可提高临床的影像学诊断率,为临床提供更多的诊疗信息。     

Regularity in Endomorphism Rings

The unique largest regular ideal Reg(A, A) in the endomorphism ring End(A) is computed for abelian groups A using the general tools developed in [7 Kasch , F. , Mader , A. ( 2005 ). Regularity and substructures of hom . Communications in Algebra 34 : 1459 – 1478 .[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]]. This generalizes earlier results on groups with regular endomorphism ring. Interesting questions remain for a very special class of mixed abelian groups.     

A Generalization of Divided Domains and Its Connection to Weak Baer Going-Down Rings

Many results on going-down domains and divided domains are generalized to the context of rings with von Neumann regular total quotient rings. A (commutative unital) ring R is called regular divided if each P ∈ Spec(R)?(Max(R) ∩ Min(R)) is comparable with each principal regular ideal of R. Among rings having von Neumann regular total quotient rings, the regular divided rings are the pullbacks K× _K/P D where K is von Neumann regular, P ∈ Spec(K) and D is a divided domain. Any regular divided ring (for instance, regular comparable ring) with a von Neumann regular total quotient ring is a weak Baer going-down ring. If R is a weak Baer going-down ring and T is an extension ring with a von Neumann regular total quotient ring such that no regular element of R becomes a zero-divisor in T, then R ? T satisfies going-down. If R is a weak Baer ring and P ∈ Spec(R), then R + PR _(P) is a going-down ring if and only if R/P and R _P are going-down rings. The weak Baer going-down rings R such that Spec(R)?Min(R) has a unique maximal element are characterized in terms of the existence of suitable regular divided overrings.     

Volume estimates for sections of certain convex bodies

This paper deals with volume estimates for hyperplane sections of the simplex and for m‐codimensional sections of powers of m‐dimensional Euclidean balls. In the first part we consider sections through the centroid of the n‐dimensional regular simplex. We state a volume formula and give a lower bound for the volume of sections through the centroid. In the second part we study the extremal volumes of m‐codimensional sections “perpendicular” to of unit balls in the space for all . We give volume formulas and use them to show that the normal vector (1, 0, …, 0) yields the minimal volume. Furthermore we give an upper bound for the ‐dimensional volumes for natural numbers . This bound is asymptotically attained for the normal vector as .     

Left SF-Rings and Regular Rings

A ring R is called a left (right) SF-ring if all simple left (right) R-modules are flat. It is known that von Neumann regular rings are left and right SF-rings. In this article, we study the regularity of left SF-rings and we prove the following: 1) if R is a left SF-ring whose all complement left (right) ideals are W-ideals, then R is strongly regular; 2) if R is a left SF-ring whose all maximal essential right ideals are GW-ideals, then R is regular.     

On Mono- and Epimorphisms in Varieties of Ordered Algebras

We study morphisms in varieties of ordered universal algebras. We prove that (i) monomorphisms are precisely the injective homomorphisms and that (ii) every regular monomorphism is an order embedding, but the converse is not true in general. We also give a necessary and sufficient condition for a morphism to be a regular epimorphism. Finally, we discuss factorizations in such varieties.     

Tilting Modules Over Quasi-Hereditary Nakayama Algebras #

The structure of Ringel duals of quasi-hereditary Nakayama algebras and of quasi-hereditary left serial algebras is described.     

The Socle and Semisimplicity of a Kumjian–Pask Algebra

The Kumjian–Pask algebra KP(Λ) is a graded algebra associated to a higher-rank graph Λ and is a generalization of the Leavitt path algebra of a directed graph. We analyze the minimal left ideals of KP(Λ), and identify its socle as a graded ideal by describing its generators in terms of a subset of vertices of the graph. We characterize when KP(Λ) is semisimple, and obtain a complete structure theorem for a semisimple Kumjian–Pask algebra. As a consequence of this structure theorem, every semisimple Kumjian–Pask algebra can be obtained as a Leavitt path algebra of a directed graph.