A GENERALIZATION OF THE THEORY OF STANDARDLY STRATIFIED ALGEBRAS I: STANDARDLY STRATIFIED RINGOIDS
Por:
Mendoza, O., Ortiz, M., Saenz, C., Santiago, V.
Publicada:
1 ene 2022
Ahead of Print:
1 ene 2020
Categoría:
Mathematics (miscellaneous)
Resumen:
We extend the classical notion of standardly stratified k-algebra
(stated for finite dimensional k-algebras) to the more general class of
rings, possibly without 1, with enough idempotents. We show that many of
the fundamental results, which are known for classical standardly
stratified algebras, can be generalized to this context. Furthermore,
new classes of rings appear as: ideally standardly stratified and
ideally quasi-hereditary. In the classical theory, it is known that
quasi-hereditary and ideally quasi-hereditary algebras are equivalent
notions, but in our general setting, this is no longer true. To develop
the theory, we use the well-known connection between rings with enough
idempotents and skeletally small categories (ringoids or rings with
several objects).
Filiaciones:
Mendoza, O.:
Instituto de Matemáticas, Universidad Nacional Autónoma de México, Mexico City, Mexico
Circuito Exterior Ciudad Universitaria, Mexico City, C.P. 04510, Mexico
Ortiz, M.:
Universidad Autónoma Del Estado de México, Mexico City, Mexico
Saenz, C.:
Circuito Exterior Ciudad Universitaria, Mexico City, C.P. 04510, Mexico
Departamento de Matemáticas, Universidad Nacional Autónoma de México, Mexico City, Mexico
Santiago, V.:
Circuito Exterior Ciudad Universitaria, Mexico City, C.P. 04510, Mexico
Departamento de Matemáticas, Universidad Nacional Autónoma de México, Mexico City, Mexico
Green Submitted, All Open Access; Green
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