Titlebook: Algebra; Serge Lang Textbook 2002Latest edition Springer Science+Business Media New York 2002 Algebra Textbook.Category theory.Textbook.al

創(chuàng)作

https://doi.org/10.1007/978-3-322-92929-7eigenvalues and the characteristic polynomial. The main theorem can be viewed as giving an example for the general structure theorem of modules over a principal ring. In the present case, the principal ring is the polynomial ring .[.] in one variable.

FUSE

Galois Theoryhe Galois group and their classifications. We shall mention a number of fundamental unsolved problems, the most notable of which is whether given a finite group G, there exists a Galois extension of Q having this group as Galois group. Three surveys give recent points of view on those questions and sizeable bibliographies:

nascent

Extensions of Ringsly at how the Galois automorphisms operate on prime ideals or the residue class fields. The two examples given after Theorem 2.9 show the importance of working over rings, to get families of extensions in two very different contexts.

ANTI

易于出錯

Representation of One Endomorphismeigenvalues and the characteristic polynomial. The main theorem can be viewed as giving an example for the general structure theorem of modules over a principal ring. In the present case, the principal ring is the polynomial ring .[.] in one variable.

Eeg332

相信

Polynomials certain statements of algebra are universally true. To prove them, one proves them first for elements of a polynomial ring over Z, and then one obtains the statement in arbitrary fields (or commutative rings as the case may be) by specialization. The Cayley-Hamilton theorem of Chapter XV, for instance, can be proved in that way.

眼界

Textbook 2002Latest editionics books: "Lang‘s Algebra changed the way graduate algebra is taught, retaining classical topics but introducing language and ways of thinking from category theory and homological algebra. It has affected all subsequent graduate-level algebra books.".From MathSciNet‘s review of the first edition:."