2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/61790Regular and higher regular graded algebras (in simplest case satisfying Von Neumann regularity $Θ_{1}Θ_{2}Θ_{1}=Θ_{1}$ instead of anticommutativity) are introduced and their properties are studied. They are described in terms of obstructed categories with nonclosed invertible and noninvertible morphisms for which generalized (obstructed) functors and natural transformations are given. Regular algebras and bialgebras are considered with examples. Corresponding regularizations of the cross product and Wick algebras are made.13 pages, AmSLaTeX (for other formats see http://gluon.physik.uni-kl.de/~duplij)Quantum AlgebraHigh Energy Physics - TheoryMathematical PhysicsGeneral TopologyK-Theory and HomologyRings and Algebrastext