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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]

Bi-Koszul algebras, including two classes of non-Koszul Artin-Schelter regular algebras of global dimension 4, were a class of graded algebras with non-pure resolutions, introduced in [8]. There is a natural question: can we construct bi-Koszul algebras from algebras with pure resolutions? In this paper, we study this question in terms of normal extensions and Ore extensions. More precisely, we attempt to obtain bi-Koszul algebras from algebras with pure resolutions by these two kinds of extensions. Furthermore, some homological properties of bi-Koszul algebras obtained in such ways are discussed. [ABSTRACT FROM AUTHOR]

In this paper, we extend the notion of n-isoclinism to the class of all pairs of groups (G,M), where M is a normal subgroup of a group G. The details of that notion are studied and some equivalent conditions are given for two pairs of groups to be n-isoclinic. In addition, the concept of subgroup- and quotient-irreducibility for a pair of groups is defined and we derive how to see whether (G,M) has a pair of subgroups or a pair of factor groups n-isoclinic with (G,M). [ABSTRACT FROM AUTHOR]

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]