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In this note, we slightly generalize Theorem 2 in the paper by M. Tunç and point out that the assumption of Theorem 3 is not sufficient. A misuse of the term 'mean' is also discussed.

It is a well known result in the covering groups that a subgroup $G$ of the fundamental group at the identity of a semi-locally simply connected topological group determines a covering morphism of topological groups with characteristic group $G$. In this paper we generalize this result to a large class of algebraic objects called topological groups with operations, including topological groups. We also give the cover of crossed modules within topological groups with operations., Comment: 15 pages, research paper, LaTeX2e, xypic

We use pseudo-Anosov homeomorphisms of surfaces in order to prove that the first order theory of non abelian free groups, $T_{fg}$, is $n$-ample for any $n\in\omega$. This result adds to the work of Pillay, that proved that $T_{fg}$ is non CM -trivial. The sequence witnessing ampleness is a sequence of primitive elements in $F_{\omega}$. Our result provides an alternative proof to the main result of a preprint by Ould Houcine-Tent. We also add an appendix in which we make a few remarks on Sela's paper on imaginaries in torsion free hyperbolic groups. In particular we give alternative transparent proofs concerning the non-elimination of certain imaginaries., Comment: 22 pages, 2 figures. To appear in the Turkish Journal of Mathematics. Replaces arXiv:1205.4662

In this paper, we introduce and study V -Gorenstein at modules and show the stability of the category of V -Gorenstein at modules. We investigate the existence of V -Gorenstein at covers and V -Gorenstein at preenvelopes for any left R -module. Also we prove that ( V - GF ;V - GF ? ) is a perfect hereditary cotorsion pair in B l ( R) , where V - GF stands the class of V -Gorenstein at left R -modules and B l ( R) is the left Bass class. Some applications are given.

In this paper, we introduce and study Ext-strongly Gorenstein projective modules. We prove that the class of Ext-strongly Gorenstein projective modules is projective resolving. Moreover, we consider Ext-strongly Gorenstein projective precovers.

This paper is concerned with almost para-complex structures on Walker 4-manifolds. For these structures, we study some problems of Kahler manifolds. We also give an example of a flat almost para-complex manifold, which consists of a nonintegrable almost para-complex structure on Walker 4-manifolds.

WOS: 000335286000005, The index and the period of an element a of a finite semigroup are defined as the smallest values of m >= 1 and r >= 1 such that a(m+r) = a(m), respectively. If m = 1 then a is called an element of index 1. The aim of this paper is to find some properties of the elements of index 1 in T-n, which we call transformations of index 1.

Let M be a smooth manifold with Finsler metric F, and let TM° be the slit tangent bundle of M with a generalized Riemannian metric G, which is induced by F. In this paper, we extract many natural foliations of (TM°,G) and study some of their geometric properties. Next we use this approach to obtain new characterizations of Finsler manifolds with positive constant curvature.

Let G be a finite group. In this paper, we introduce the concept of super generalized supersolvably embedded subgroup of a group G and give a new characterization of the generalized hypercenter of G.

In this paper we introduce the notions of semi-slant and bi-slant submanifolds of an almost contact 3-structure manifold. We give some examples and characterization theorems about these submanifolds. Moreover, the distributions of semi-slant submanifolds of 3-cosymplectic and 3-Sasakian manifolds are studied. ϕi)i=1;2;3 and the vector elds should be slant or invariant with respect to all of the ϕi's. Therefore, it is a generalization of invariant, anti-invariant, slant, semi-slant, and bi-slant submanifolds in almost contact metric 3-structures and we denote them by 3- semi-slant and 3-bi-slant submanifolds. Following the approaches of (3, 13), we characterized 3-bi-slant and 3-semi-slant submanifolds and studied geometric properties of distributions of these submanifolds where the ambient manifolds are 3-Sasakian or 3-cosymplectic. It should be noted that, in the denition of semi-slant

In this paper, we consider Finsler metrics defined by a Riemannian metric and a 1-form on a manifold. We study these metrics with vanishing S-curvature. We find some conditions under which such a Finsler metric is Berwaldian or locally Minkowskian.

A classical result of Posner states that the existence of a nonzero centralizing derivation on a prime ring forces the ring to be commutative. In this paper we extend Posner's result to generalized derivations centralizing on Jordan ideals of rings with involution and discuss the related results. Moreover, we provide examples to show that the assumed restriction cannot be relaxed.

In this paper, we define the concept of almost product Riemannian submersion between almost product Riemannian manifolds. We introduce slant submersions from almost product Riemannian manifolds onto Riemannian manifolds. We give examples and investigate the geometry of foliations that arise from the definition of a Riemannian submersion. We also find necessary and sufficient conditions for a slant submersion to be totally geodesic.

In this paper, we discuss the Bass class and the Auslander class with respect to a semidualizing module over an associative ring. Let SCR be a semidualizing module, we proved that the Bass class BC (R) is a right orthogonal subcategory of some right R-module; and that the Auslander class AC (S) is a left orthogonal subcategory of the character module of some left S-module. As an application, we introduce the notion of the minimal semidualizing module, and get a one to one correspondence between the isomorphism classes of minimal semidualizing R-modules and maximal classes among coresolving preenvelope classes of Mod R with the same Ext-projective generators in gen* R.

This paper investigates the structure theory of Zd-central simple graded algebras and gives the complete decomposition into building block algebras. The results are also applied to generalized Clifford algebras, which are motivating examples of Zd-central simple graded algebras.