منابع مشابه
On Semilocal Modules and Rings
It is well-known that a ring R is semiperfect if and only if RR (or RR) is a supplemented module. Considering weak supplements instead of supplements we show that weakly supplemented modules M are semilocal (i.e., M/Rad(M) is semisimple) and that R is a semilocal ring if and only if RR (or RR) is weakly supplemented. In this context the notion of finite hollow dimension (or finite dual Goldie d...
متن کاملTits Indices over Semilocal Rings
We present a simplified version of Tits’ proof of the classification of semisimple algebraic groups, which remains valid over semilocal rings. We also provide explicit conditions on anisotropic groups to appear as anisotropic kernels of semisimple groups of a given index.
متن کاملBraid Group Actions and Tensor Products
We define an action of the braid group of a simple Lie algebra on the space of imaginary roots in the corresponding quantum affine algebra. We then use this action to determine an explicit condition for a tensor product of arbitrary irreducible finite–dimensional representations is cyclic. This allows us to determine the set of points at which the corresponding R–matrix has a zero. 0. Introduct...
متن کاملbivariations and tensor products
the ordinary tensor product of modules is defined using bilinear maps (bimorphisms), that are linear in eachcomponent. keeping this in mind, linton and banaschewski with nelson defined and studied the tensor product in an equational category and in a general (concrete) category k, respectively, using bimorphisms, that is, defined via the hom-functor on k. also, the so-called sesquilinear, or on...
متن کاملReal Closures of Semilocal Rings, and Extension of Real Places
(A) All rings in this announcement are commutative and with 1. For any ring K we denote by W(K) the Witt ring of nondegenerate symmetric bilinear forms over K. DEFINITION 1. A signature o of K is a ring homomorphism from W(K) to Z. REMARK 1. If K is a field, the signatures correspond uniquely with the orderings of K [3], [9]. Thus Theorem 1 below generalizes the main results of Artin-Schreier's...
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: Michigan Mathematical Journal
سال: 1976
ISSN: 0026-2285
DOI: 10.1307/mmj/1029001571