Commutative quartic P-Galois extensions over a field of characteristic 2

Let A/R be a ring extension and P a subset of Hom(A(R),A(R)). In his paper [5], K. Kishimoto introduced the notion of a P-Galois extension and gave several basic properties of these extensions. The author showed that these extensions are closely related to Hopf Galois extensions and the structure of quadratic or cubic P-Galois extensions over a field were given in [9] and [10]. Recently,the author classify commutative quartic P-Galois extensions over a field of characteristic not 2 in [11]. Continuing [11], we treat commutative quartic P-Galois extensions over a field of characteristic 2

Derivations on Matrix Near-Ring

The existence of a derivation in a near-ring is not known. We construct derivations on 2×2 matrix near-ring in the sense of [MW]

Smash product extensions of separable algebras

Let A be a bialgebra and let S be a right A-comodule algebra which has an A-comodule subalgebra T with common identity. We show that if S is a separable extension of T, then for a left A-module algebra K, K♯S is a separable extension of K♯T. Similar result holds for left A-module algebras and right A-comodule algebras

Constrained Inefficiency and Optimal Taxation with Uninsurable Risks

Should capital and labor be taxed, and if so how when individuals' labor and capital income are subject to uninsurable idiosyncratic risks? In a two period general equilibrium model with production, we first show that reducing investment is welfare improving if households are homogeneous enough ex ante. On the other hand, when the degree of heterogeneity is sufficientlyhigh a welfare improvement is achieved by increasing investment, even if the investment level is already higher than at the e¢ cient allocation obtained when full insurance markets were available. Consequently, the optimal capital tax rate might be negative. We derive a decomposition formula of the e¤ects of the tax which allow us to determine how the sign of optimal tax on capital and labor depends both on the nature of the shocks and the degree of heterogeneity among consumers as well as on the way in which the tax revenue is allocated.

Optimal taxation and constrained inefficiency in an infinite-horizon economy with incomplete markets

We study the dynamic Ramsey problem of finding optimal public debt and linear taxes on capital and labor income within a tractable infinite horizon model with incomplete markets. With zero public expenditure and debt, it is optimal to tax the risky labor income and subsidize capital, while a positive amount of public debt is welfare improving. A steady state optimality condition is derived which implies that the tax on capital is positive, when savings are sufficiently inelastic to returns. A calibration of our model to the US economy indicates positive optimal taxes and a small but positive optimal debt level.incomplete markets; Ramsey equilibrium; optimal taxation; optimal public debt; constrained inefficiency