Basic Theory of Additive Abelian Groups
ثبت نشده
چکیده
In this chapter we discuss cyclic groups, the quotient group construction, the direct sum construction and the first isomorphism theorem, in the context of additive abelian groups; we also discuss free modules. These concepts are necessary, as well as the matrix theory of Chapter 1, for the study of finitely generated abelian groups in Chapter 3. At the same time the material provides the reader with a taster for general group theory.
منابع مشابه
A compactness argument in the additive theory and the polynomial method
In this expository paper we collect some combinatorial problems in the additive theory that can be easily solved in ordered Abelian groups. We study how such results, obtained by simple combinatorial arguments, can be extended to other Abelian groups. In many cases, best results can be obtained with the help of the so-called polynomial method that has evolved to a very powerful tool in the addi...
متن کاملThe Character Group of Q
The characters of a finite abelian group G are the homomorphisms from G to the unit circle S1 = {z ∈ C : |z| = 1}. Two characters can be multiplied pointwise to define a new character, and under this operation the set of characters of G forms an abelian group, with identity element the trivial character, which sends each g ∈ G to 1. Characters of finite abelian groups are important, for example...
متن کاملContinuous cohomology and homology of profinite groups
Let G be a profinite group with a countable basis of neighborhoods of the identity. A cohomology and homology theory for the group G with non-discrete topological coefficients is developed, improving previous expositions of the subject (see [Wi], [R–Z] and [S-W]). Though the category of topological G-modules considered is additive but not abelian, there is a theory of derived functors. All stan...
متن کاملIntroduction to Abelian and Derived Categories
This is an account of three 1-hour lectures given at the Instructional Conference on Representation Theory of Algebraic Groups and Related Finite Groups, Isaac Newton Institute, Cambridge, 6–11 January 1997. In section 1, we define abelian categories following Grothendieck [12]. We then characterize module categories among abelian categories. Finally we sketch a proof of Mitchell’s full embeddi...
متن کاملQuadratic and Hermitian Forms in Additive and Abelian Categories
During the last few years several papers concerned with the foundations of the theory of quadratic forms over arbitrary rings with involution have appeared. It is not necessary to give detailed references, in particular one thinks of the well known work of Bak [l], Bass [3], Karoubi, Knebusch [ll, 121, Ranicki, Vaserstein, and C. T. C. Wall. During the same period a number of problems quite sim...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2017