Reducing submodules of Hilbert modules and Chevalley-Shephard-Todd theorem

Shephard-todd-chevalley Theorem for Skew Polynomial Rings

We prove the following generalization of the classical ShephardTodd-Chevalley Theorem. Let G be a finite group of graded algebra automorphisms of a skew polynomial ring A := kpij [x1, · · · , xn]. Then the fixed subring A has finite global dimension if and only if G is generated by quasireflections. In this case the fixed subring A is isomorphic a skew polynomial ring with possibly different pi...

The Chevalley-shephard-todd Theorem for Finite Linearly Reductive Group Schemes

We generalize the classical Chevalley-Shephard-Todd theorem to the case of finite linearly reductive group schemes. As an application, we prove that every scheme X which is étale locally the quotient of a smooth scheme by a finite linearly reductive group scheme is the coarse space of a smooth tame Artin stack (as defined by Abramovich, Olsson, and Vistoli) whose stacky structure is supported o...

N ov 2 00 8 EXTENDING THE COINVARIANT THEOREMS OF CHEVALLEY , SHEPHARD – TODD , MITCHELL , AND SPRINGER

We extend in several directions invariant theory results of Chevalley, Shephard and Todd, Mitchell and Springer. Their results compare the group algebra for a finite reflection group with its coinvariant algebra, and compare a group representation with its module of relative coinvariants. Our extensions apply to arbitrary finite groups in any characteristic.

dedekind modules and dimension of modules

در این پایان نامه، در ابتدا برای مدول ها روی دامنه های پروفر شرایط معادل به دست آورده ایم و خواصی از ددکیند مدول ها روی دامنه های پروفر مشخص کرده ایم. در ادامه برای ددکیند مدول های با تولید متناهی روی حلقه های به طور صحیح بسته شرایط معادل به دست آورده ایم و ددکیند مدول های ضربی را مشخص کرده ایم. گزاره هایی در مورد بعد ددکیند مدول ها بیان کرده ایم. در پایان، قضایای lying over و going down را برا...

Submodules of Secondary Modules