A note on extensions of algebraic and formal groups II.
A note on finitely generated commutative rings
A note on formal groups and zeta functions.
A note on formal power series
In this note we investigate a relationship between the boundary behavior of power series and the composition of formal power series. In particular, we prove that the composition domain of a formal power series is convex and balanced which implies that the subset consisting of formal power series which can be composed by a formal power series possesses such properties. We also provide a necessary and sufficient condition for the superposition operator to map into itself or to map into...
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 generalized primary rings
A note on imperfect monomial curves in
A note on indecomposable modules over valuation domains
A note on indecomposable projective modules
A note on linear derivations
At first we prove some results on a general polynomial derivation using few results of linear derivation. Then we study the ring of constants of a linear derivation for some rings. We know that any linear derivation is a nonsimple derivation. In the last section we find the smallest integer such that the polynomial ring in variables is -differentially simple, all derivations are nonsimple and the derivations set contains a linear derivation.
A note on local Noether lattices
A note on Nakai’s conjecture for the ring
A note on perfect modules over crossed products
A note on perfect rings.
A note on PG-modules.
A note on Poisson derivations
Free Poisson algebras are very closely connected with polynomial algebras, and the Poisson brackets are used to solve many problems in affine algebraic geometry. In this note, we study Poisson derivations on the symplectic Poisson algebra, and give a connection between the Jacobian conjecture with derivations on the symplectic Poisson algebra.
A note on power invariant rings.
A note on projective modules and multiplication modules
A Note on Projective Modules Over Polynomial Rings.
A note on quasi-complete local rings