We give a classification of Hopf real hypersurfaces in complex hyperbolic two-plane Grassmannians
${\rm SU}_{2,m}/S(U_2{\cdot}U_m)$ with commuting conditions between the restricted normal Jacobi operator $\overline{R}_N\phi$ and the shape operator $A$ (or the Ricci tensor $S$)., Doo Hyun Hwang, Eunmi Pak, Changhwa Woo., and Obsahuje bibliografii
A weak basis of a module is a generating set of the module minimal with respect to inclusion. A module is said to be regularly weakly based provided that each of its generating sets contains a weak basis. We study (1) rings over which all modules are regularly weakly based, refining results of Nashier and Nichols, and (2) regularly weakly based modules over Dedekind domains., Michal Hrbek, Pavel Růžička., and Seznam literatury
Let R be a commutative Noetherian ring and let C be a semidualizing R-module. We prove a result about the covering properties of the class of relative Gorenstein injective modules with respect to C which is a generalization of Theorem 1 by Enochs and Iacob (2015). Specifically, we prove that if for every Gc-injective module G, the character module G+ is Gc-flat, then the class GIc(R) Ac(R) is closed under direct sums and direct limits. Also, it is proved that under the above hypotheses the class GIc(R) Ac(R) is covering., Elham Tavasoli, Maryam Salimi., and Obsahuje bibliografii
A graph is called distance integral (or D-integral) if all eigenvalues of its distance matrix are integers. In their study of D-integral complete multipartite graphs, Yang and Wang (2015) posed two questions on the existence of such graphs. We resolve these questions and present some further results on D-integral complete multipartite graphs. We give the first known distance integral complete multipartite graphs {K_{{p_1},{p_2},{p_3}}} with p1 < p2 < p3, and {K_{{p_1},{p_2},{p_3},{p_4}}} with p1 < p2 < p3 < p4, as well as the infinite classes of distance integral complete multipartite graphs {K_{{a_1}{p_1},{a_2}{p_2},...,{a_s}{p_s}}} with s = 5, 6., Pavel Híc, Milan Pokorný., and Obsahuje seznam literatury
This paper is about some geometric properties of the gluing of order k in the category of Sikorski differential spaces, where k is assumed to be an arbitrary natural number. Differential spaces are one of possible generalizations of the concept of an infinitely differentiable manifold. It is known that in many (very important) mathematical models, the manifold structure breaks down. Therefore it is important to introduce a more general concept. In this paper, in particular, the behaviour of kth order tangent spaces, their dimensions, and other geometric properties, are described in the context of the process of gluing differential spaces. At the end some examples are given. The paper is self-consistent, i.e., a short review of the differential spaces theory is presented at the beginning., Krzysztof Drachal., and Obsahuje seznam literatury
A subalgebra H of a finite dimensional Lie algebra L is said to be a SCAP-subalgebra if there is a chief series 0 = L0 \subset L1 \subset...\subset Lt = L of L such that for every i = 1, 2,..., t, we have H + Li = H + Li-1 or H ∩ Li = H ∩ Li-1. This is analogous to the concept of SCAP-subgroup, which has been studied by a number of authors. In this article, we investigate the connection between the structure of a Lie algebra and its SCAP-subalgebras and give some sufficient conditions for a Lie algebra to be solvable or supersolvable., Sara Chehrazi, Ali Reza Salemkar., and Obsahuje seznam literatury