On Strong Monomorphisms and Strong Epimorphisms

On Strong Monomorphisms and Strong Epimorphisms

M. A. Al Shumrani Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia Correspondence should be addressed to M. A. Al Shumrani, [email protected] Received 10 March 2010; Accepted 5 May 2010 Academic Editor: Mihai Putinar Copyright q 2010 M. A. Al Shumrani. This is an open access article distributed under the Creative Commons Attribution License,...

On Epimorphisms and Monomorphisms of Hopf Algebras

We notice that for a Hopf algebra H , its antipode S is both an epimorphism and a monomorphism from H to H in the category of Hopf algebras over a field. Together with the existence of Hopf algebras with non-injective or non-surjective antipode, this proves the existence of non-surjective epimorphisms and non-injective monomorphisms in the category of Hopf algebras. Using Schauenburg’s free Hop...

Equivariant Homotopy Epimorphisms, Homotopy Monomorphisms and Homotopy Equivalences

?-Independent and Dissociate Sets on Compact Commutative Strong Hypergroups

In this paper we define ?-independent (a weak-version of independence), Kronecker and dissociate sets on hypergroups and study their properties and relationships among them and some other thin sets such as independent and Sidon sets. These sets have the lacunarity or thinness property and are very useful indeed. For example Varopoulos used the Kronecker sets to prove the Malliavin theorem. In t...

On multiplicative (strong) linear preservers of majorizations

‎In this paper, we study some kinds of majorizations on $textbf{M}_{n}$ and their linear or strong linear preservers. Also, we find the structure of linear or strong linear preservers which are multiplicative, i.e.  linear or strong linear preservers like $Phi $ with the property $Phi (AB)=Phi (A)Phi (B)$ for every $A,Bin textbf{M}_{n}$.