Abstract
The concept of modulation is generalized to pseudo-modulation and its subclasses including pre-modulation, generalized modulation and regular modulation. The motivation is to de¯ne the valued analogue of natural quiver, called natural valued quiver, of an artinian algebra so as to correspond to its valued Ext-quiver when this algebra
is not k-splitting over the ¯eld k. Moreover, we illustrate the relation between the
valued Ext-quiver and the natural valued quiver.

The interesting fact we ¯nd is that the representation categories of a pseudomodulation and of a pre-modulation are equivalent respectively to that of a tensor
algebra of A-path type and of a generalized path algebra. Their examples are given respectively from two kinds of artinian hereditary algebras. Furthermore, the isomorphism theorem is given for normal generalized path algebras with ¯nite (acyclic) quivers and normal pre-modulations.

Four examples of pseudo-modulations are given: (i) group species in mutation theory as a semi-normal generalized modulation; (ii) viewing a path algebra with loops as a pre-modulation with valued quiver which has not loops; (iii) di®erential pseudo-modulation and its relation with di®erential tensor algebras; (iv) a pseudo-
modulation is considered as a free graded category.

2010 Mathematics Subject Classi¯cations: 16G10; 16G20
keywords: pseudo-modulation; tensor algebra; natural valued quiver; valued Ext-quiver;
artinian algebra; generalized path algebra