Titlebook: Mathematical Structures; From Linear Algebra Joachim Hilgert Textbook 20241st edition The Editor(s) (if applicable) and The Author(s), und

橢圓

使混合

Transfer of Arguments and StructuresIn this chapter, we illustrate the transfer of arguments and structural elements to other areas with two examples. Homological algebra as a technology for structural comparison and the concept of a group object for the formalization of symmetries.

思想

Rings deeper into ring theory and discuss some interesting and fundamental structural properties of rings that we will need in later applications. At the same time, these considerations illustrate how to deal with algebraic structures.

審問,審訊

Modulesbroad that it can form the framework for the relevant functions of almost all central areas of mathematics. On the other hand, the module structure is also so rich that it allows a significant theory that has extremely interesting applications. A key goal of this chapter is to provide convincing evidence for these two claims.

感激小女

Specialization, Generalization and Unification of Structureslist of well-motivated structures that have not yet been listed in the first two parts. Otherwise, e.g., the absence of . would be inexcusable. Rather, the aim is to convey a sense that the structural considerations of the first two parts allow us to place a multitude of mathematical terms without much effort.

努力趕上

978-3-662-69411-4The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer-Verlag GmbH, DE

反話

灰姑娘

adumbrate

Sheavesthe objects assigned to two open sets should be compatible with each other when the open sets intersect. For continuous functions, this is the case since restrictions of continuous functions to the intersection are also continuous.

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