Titlebook: Algebra II; Textbook for Student Alexey L. Gorodentsev Textbook 2017 Springer International Publishing AG 2017 Fields.Rings.Modules.Groups.

厌烦

https://doi.org/10.1007/978-3-8350-9279-2Everywhere in this section, the term “ring” means by default a commutative ring with unit. All ring homomorphisms are assumed to map the unit to the unit.

ALIAS

大包裹

https://doi.org/10.1007/978-3-8350-9279-2Everywhere in this chapter we assume by default that the ground field . is algebraically closed.

阻止

https://doi.org/10.1007/978-3-8350-9279-2Recall that a field extension . is said to be . of . . if . has dimension . < . as a vector space over .. We write . in this case.

草本植物

conduct

Tensor Algebras,Let . be a vector space over an arbitrary field .. We write . for the tensor product of . copies of . and call it the . of ..

牛马之尿

音的强弱

Basic Notions of Representation Theory,Given a set . and a field ., let us write . for the vector space with basis . over .. It is formed by the formal linear combinations .. ⋅ . of elements . ∈ . with coefficients ., all but a finite number of which vanish. By definition, the . . spanned by the set . is the tensor algebra . of the vector space ..

性满足

Representations of Finite Groups in Greater Detail,Everywhere in this section, we write by default . for an arbitrary finite group and . for an algebraically closed field such that ..

absolve

-Modules,Everywhere in this section we assume by default that . is a field of characteristic zero.