Quadratic categories and square rings
نویسندگان
چکیده
منابع مشابه
Quadratic Rings
From an abstract algebraic perspective, an explanation for this can be given as follows: since √ D is irrational, the polynomial t −D is irreducible over Q. Since the ring Q[t] is a PID, the irreducible element t − D generates a maximal ideal (t−D), so that the quotient Q[t]/(t−D) is a field. Moreover, the map Q[ √ D]→ Q[t]/(t −D) which is the identity on Q and sends √ D 7→ t is an isomorphism ...
متن کاملOn the square root of quadratic matrices
Here we present a new approach to calculating the square root of a quadratic matrix. Actually, the purpose of this article is to show how the Cayley-Hamilton theorem may be used to determine an explicit formula for all the square roots of $2times 2$ matrices.
متن کاملInvariant Rings through Categories
We formulate a notion of “geometric reductivity” in an abstract categorical setting which we refer to as adequacy. The main theorem states that the adequacy condition implies that the ring of invariants is finitely generated. This result applies to the category of modules over a bialgebra, the category of comodules over a bialgebra, and the category of quasi-coherent sheaves on an algebraic sta...
متن کاملZero Square Rings
A ring R for which x = 0 for all x e R is called a zerosquare ring. Zero-square rings are easily seen to be locally nilpotent. This leads to two problems: (1) constructing finitely generated zero-square rings with large index of nilpotence, and (2) investigating the structure of finitely generated zerosquare rings with given index of nilpotence. For the first problem we construct a class of zer...
متن کاملFaithfully Quadratic Rings
The aim of this paper is to lay the groundwork for a theory of quadratic forms over several significant, and quite extensive, classes of preordered rings. By “quadratic forms” we understand, here, diagonal quadratic forms with unit coefficients; and “ring” stands for commutative unitary ring where 2 in invertible. We achieve this by the use, in the ring context, of our abstract theory of quadra...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 1997
ISSN: 0022-4049
DOI: 10.1016/s0022-4049(97)00130-8