In the present paper we describe a class of Φ-Auslander-Yoneda algebras over K[x]/(xn) in terms of quivers with relations, and prove that they are actually cellular algebras in the sense of Graham and Lehrer. [ABSTRACT FROM AUTHOR]
In this paper, first we show that the categories of semihypergroups and hypergroups have not free objects. Next we give the notion of weak free semihypergroups for the classes of semihypergroups and extension complete semihypergroups (ECS). Also, we give a necessary and sufficient condition for a semihypergroup for being weak free semihypergroups in the category ECS. Finally, the existence of proper weak free objects in ECS is proved. [ABSTRACT FROM AUTHOR]
*GROUP theory, *MATHEMATICAL analysis, *NUMERICAL analysis, *MATHEMATICAL proofs, *SET theory
Abstract
We take in this paper an arbitrary class $\mathcal{K}$ of groups as a base, and define a radical property 풫 for which every group in $\mathcal{K}$ is 풫-semisimple. This is called the upper radical property determined by the class $\mathcal{K}$. At the same time, we define a radical property 풫 for which every group in $\mathcal{K}$ is a 풫-radical group. This is called the first lower radical property determined by the class $\mathcal{K}$. Also, we give another construction leading to the second lower radical property which is proved to be identical with the first one. [ABSTRACT FROM AUTHOR]