人充满活力
发表于 2025-3-23 13:02:02
Groups,In this chapter we introduce groups and prove some of the basic theorems in group theory. One of these, the structure theorem for finitely generated abelian groups, we do not prove here but instead derive it as a corollary of the more general structure theorem for finitely generated modules over a PID (see Theorem 3.7.22).
流动性
发表于 2025-3-23 13:51:44
Rings,(1.1) Definition. . ring (.,+,) . +: . ×.→. (.) . : . ×.→. (.) ..
混合,搀杂
发表于 2025-3-23 21:47:07
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AWL
发表于 2025-3-23 23:50:03
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demote
发表于 2025-3-24 05:28:55
Group Representations,We begin by defining the objects that we are interested in studying. Recall that if . is a ring and . is a group, then .(.) denotes the group ring of . with coefficients from .. The multiplication on .(.) is the convolution product (see Example 2.1.10 (15)).
碎石头
发表于 2025-3-24 06:47:34
Graduate Texts in Mathematicshttp://image.papertrans.cn/a/image/152413.jpg
Pantry
发表于 2025-3-24 11:20:00
Algebra978-1-4612-0923-2Series ISSN 0072-5285 Series E-ISSN 2197-5612
Ganglion-Cyst
发表于 2025-3-24 15:37:58
Linear Algebra,al form theory for a linear transformation from a vector space to itself. The fundamental results will be presented in Section 4.4. We will start with a rather detailed introduction to the elementary aspects of matrix algebra, including the theory of determinants and matrix representation of linear
抛媚眼
发表于 2025-3-24 21:37:20
Matrices over PIDs,y if the .[.]-modules . and . are isomorphic (Theorem 4.4.2). Since the structure theorem for finitely generated torsion .[.]-modules gives a criterion for isomorphism in terms of the invariant factors (or elementary divisors), one has a powerful tool for studying linear transformations, up to simil
公共汽车
发表于 2025-3-25 02:29:14
Bilinear and Quadratic Forms, means of the operations (.+.)(.)=.(.)+.(.) and (.)(.)= .(.(.)) for all .. Moreover, if . then Hom.(.)= End .(.) is a ring under the multiplication (.)(.)=.(.(.)). An .-module ., which is also a ring, is called an .-algebra if it satisfies the extra axiom .(.)=(.).=.(.) for all . ∈ . and . ∈ .. Thus