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
A note on Rees algebras and the MFMC property.
A note on rings of constants of derivations in integral domains
We observe that the characterization of rings of constants of derivations in characteristic zero as algebraically closed subrings also holds in positive characteristic after some natural adaptation. We also present a characterization of such rings in terms of maximality in some families of rings.
A note on semisimple derivations of commutative algebras
A concept of a slice of a semisimple derivation is introduced. Moreover, it is shown that a semisimple derivation d of a finitely generated commutative algebra A over an algebraically closed field of characteristic 0 is nothing other than an algebraic action of a torus on Max(A), and, using this, that in some cases the derivation d is linearizable or admits a maximal invariant ideal.
A note on the algebraic de Morgan's law
A note on the computation of multiplicities.
A note on the countable union of prime submodules.
A note on the dual of a finitely generated multiplication module