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

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https://doi.org/10.1007/978-3-8350-9279-2ape. Associated with every standard filling . of shape .?=?(..,?..,?…,?..), ..?=?., are the . ..???.. and the . ..???.. permuting the elements 1,?2,?.?,?. only within the rows and within the columns of . respectively. Thus, . and ., where..?=?(...,?...,?…,?...) is the transposed Young diagram. For example, the standard filling

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https://doi.org/10.1007/978-3-8350-9279-2.?=?sgn(.) ??. for all .?∈?... The symmetric polynomials clearly form a subring of ., whereas the alternating polynomials form a module over this subring, since the product of symmetric and alternating polynomials is alternating.

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aculty of Mathematics in the Higher School of Economics. The main content is complemented by a wealth of exercises for class discussion, some of which include comments and hints, as well as problems for?independent study..978-3-319-84507-4978-3-319-50853-5

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Symmetric Functions,.?=?sgn(.) ??. for all .?∈?... The symmetric polynomials clearly form a subring of ., whereas the alternating polynomials form a module over this subring, since the product of symmetric and alternating polynomials is alternating.

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