A note on block triangular presentations of rings and finitistic dimension
A note on centralizers.
A note on centralizers in -deformed Heisenberg algebras.
A note on clean abelian groups
A note on -cofinitely supplemented modules.
A note on coflat abelian groups
A note on commutativity of automorphisms.
A note on commutativity of nonassociative rings.
A note on -modules.
A note on derivations in semiprime rings.
A note on extending Hopf actions to rings of quotients of module algebras.
A Note on Extensions of Bear and P.p.-rings
A note on finitely generated ideal-simple commutative semirings
Many infinite finitely generated ideal-simple commutative semirings are additively idempotent. It is not clear whether this is true in general. However, to solve the problem, one can restrict oneself only to parasemifields.
A note on flat modules
A note on free direct summands.
A Note on Free Quantum Groups
We study the free complexification operation for compact quantum groups, . We prove that, with suitable definitions, this induces a one-to-one correspondence between free orthogonal quantum groups of infinite level, and free unitary quantum groups satisfying .
A note on Frobenius divided modules in mixed characteristics
If is a smooth scheme over a perfect field of characteristic , and if is the sheaf of differential operators on [7], it is well known that giving an action of on an -module is equivalent to giving an infinite sequence of -modules descending via the iterates of the Frobenius endomorphism of [5]. We show that this result can be generalized to any infinitesimal deformation of a smooth morphism in characteristic , endowed with Frobenius liftings. We also show that it extends to adic...
A note on functors that vanish on indecomposable modules.
A note on generalizations of semisimple modules
A left module over an arbitrary ring is called an -module (or an -module) if every submodule of with is a direct summand of (a supplement in, respectively) . In this paper, we investigate the various properties of -modules and -modules. We prove that is an -module if and only if , where is semisimple. We show that a finitely generated -module is semisimple. This gives us the characterization of semisimple rings in terms of -modules. We completely determine the structure of these...
A note on generalized Gorenstein dimension.