منابع مشابه
Notes on Tensor Products
Basic Definition: Let R be a commutative ring with 1. A (unital) R-module is an abelian group M together with a operation R ×M → M , usually just written as rv when r ∈ R and v ∈ M . This operation is called scaling . The scaling operation satisfies the following conditions. 1. 1v = v for all v ∈M . 2. (rs)v = r(sv) for all r, s ∈ R and all v ∈M . 3. (r + s)v = rv + sv for all r, s ∈ R and all ...
متن کاملGroups Acting on Tensor Products
Groups preserving a distributive product are encountered often in algebra. Examples include automorphism groups of associative and nonassociative rings, classical groups, and automorphism groups of p-groups. While the great variety of such products precludes any realistic hope of describing the general structure of the groups that preserve them, it is reasonable to expect that insight may be ga...
متن کاملCastelnuovo-Mumford regularity of products of monomial ideals
Let $R=k[x_1,x_2,cdots, x_N]$ be a polynomial ring over a field $k$. We prove that for any positive integers $m, n$, $text{reg}(I^mJ^nK)leq mtext{reg}(I)+ntext{reg}(J)+text{reg}(K)$ if $I, J, Ksubseteq R$ are three monomial complete intersections ($I$, $J$, $K$ are not necessarily proper ideals of the polynomial ring $R$), and $I, J$ are of the form $(x_{i_1}^{a_1}, x_{i_2}^{a_2}, cdots, x_{i_l...
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 کاملTensor Products
Let R be a commutative ring and M and N be R-modules. (We always work with rings having a multiplicative identity and modules are assumed to be unital: 1 ·m = m for all m ∈M .) The direct sum M ⊕N is an addition operation on modules. We introduce here a product operation M ⊗RN , called the tensor product. We will start off by describing what a tensor product of modules is supposed to look like....
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 Algebra
سال: 1991
ISSN: 0021-8693
DOI: 10.1016/0021-8693(91)90149-3