標(biāo)題: Titlebook: Classically Semisimple Rings; A Perspective Throug Martin Mathieu Textbook 2022 The Editor(s) (if applicable) and The Author(s), under excl [打印本頁] 作者: abandon 時(shí)間: 2025-3-21 17:26
書目名稱Classically Semisimple Rings影響因子(影響力)
作者: 無動(dòng)于衷 時(shí)間: 2025-3-21 22:34
Exchange Modules and Exchange Rings,sel, 2006) and Facchini (Module Theory: Endomorphism Rings and Direct Sum Decompositions in Some Classes of Modules. Progress in Mathematics, vol. 167. Birkh?user Verlag, Basel, 1998), which contain references to the original articles and a lot of additional information.作者: glacial 時(shí)間: 2025-3-22 02:21 作者: 熄滅 時(shí)間: 2025-3-22 06:50
Natural Deduction for Diagonal Operators,s of division rings. It is generally regarded as the first major result in the abstract structure theory of rings. In Sect. 7.2 below, we will briefly discuss the semisimplicity of group rings via Maschke’s Theorem 7.2.1. A detailed proof of the Hopkins–Levitzki theorem, already stated in ., is given in Sect. 7.3.作者: 調(diào)色板 時(shí)間: 2025-3-22 10:34
,The Artin–Wedderburn Theorem,s of division rings. It is generally regarded as the first major result in the abstract structure theory of rings. In Sect. 7.2 below, we will briefly discuss the semisimplicity of group rings via Maschke’s Theorem 7.2.1. A detailed proof of the Hopkins–Levitzki theorem, already stated in ., is given in Sect. 7.3.作者: Induction 時(shí)間: 2025-3-22 13:28
Textbook 2022ok presents the classical theory of semisimple rings from a modern, category-theoretic point of view. Examples from algebra are used to motivate the abstract language of category theory, which then provides a framework for the study of rings and modules, culminating in the Wedderburn–Artin classific作者: Induction 時(shí)間: 2025-3-22 17:44 作者: 流眼淚 時(shí)間: 2025-3-22 21:26 作者: 雪白 時(shí)間: 2025-3-23 04:30
,The Artin–Wedderburn Theorem,-dimensional algebras and to E. Artin (1927) in the general case, enables us to determine completely this class of rings from the more elementary class of division rings. It is generally regarded as the first major result in the abstract structure theory of rings. In Sect. 7.2 below, we will briefly作者: SLUMP 時(shí)間: 2025-3-23 07:19 作者: 扔掉掐死你 時(shí)間: 2025-3-23 13:35 作者: manifestation 時(shí)間: 2025-3-23 15:39 作者: Density 時(shí)間: 2025-3-23 21:23 作者: Nonconformist 時(shí)間: 2025-3-23 22:43 作者: FILLY 時(shí)間: 2025-3-24 03:11
Natural Deduction for Diagonal Operators,-dimensional algebras and to E. Artin (1927) in the general case, enables us to determine completely this class of rings from the more elementary class of division rings. It is generally regarded as the first major result in the abstract structure theory of rings. In Sect. 7.2 below, we will briefly作者: HEAVY 時(shí)間: 2025-3-24 06:59
,L’équivalence duale de catégories: ,?,t. Its main benefit lies in the fact that it allows us to convert bilinear mappings into homomorphisms of abelian groups. The relations between tensor products and homomorphism groups is fundamental and will lead us to the concept of adjoint functor in the later part of the chapter.作者: Ointment 時(shí)間: 2025-3-24 14:26 作者: 貞潔 時(shí)間: 2025-3-24 17:32
,Analysis and Synthesis in Robert Simson’s ,g .[.] is semisimple, provided . is a finite group. For any field ., the elements of . form a basis of the .-vector space .[.] and if the ring .[.] is semisimple, then it is necessarily Artinian, hence finite dimensional (Corollary . and Exercise .). As a result, we cannot expect .[.] to be semisimp作者: Herpetologist 時(shí)間: 2025-3-24 21:10 作者: 值得尊敬 時(shí)間: 2025-3-25 01:20 作者: 使成整體 時(shí)間: 2025-3-25 05:29
The Correspondence of William Burnside,Finiteness conditions on the ideal structure of a ring allow us to develop a more detailed structure theory. In the noncommutative framework, it is more natural to do this for (one-sided) modules rather than for (one-sided) ideals, so we shall follow this approach right from the beginning.作者: 調(diào)色板 時(shí)間: 2025-3-25 09:00 作者: 服從 時(shí)間: 2025-3-25 13:05
,The Misnamings of Playfair’s Axiom,In this chapter, which is at the very heart of our exposition, we shall apply module theory to study the structure of a certain class of rings; these will be termed (.) .. To this end, we will, once again, introduce some special classes of modules and investigate their properties.作者: Aggrandize 時(shí)間: 2025-3-25 16:15
Noetherian Modules,Finiteness conditions on the ideal structure of a ring allow us to develop a more detailed structure theory. In the noncommutative framework, it is more natural to do this for (one-sided) modules rather than for (one-sided) ideals, so we shall follow this approach right from the beginning.作者: 屈尊 時(shí)間: 2025-3-25 23:44
Artinian Modules,The dual condition to “ACC” is “DCC”, the descending chain condition which we shall discuss in the present chapter. The resulting modules are termed . after Emil Artin (1898–1962).作者: vascular 時(shí)間: 2025-3-26 02:22
Simple and Semisimple Modules,In this chapter, which is at the very heart of our exposition, we shall apply module theory to study the structure of a certain class of rings; these will be termed (.) .. To this end, we will, once again, introduce some special classes of modules and investigate their properties.作者: Externalize 時(shí)間: 2025-3-26 06:55 作者: 翅膀拍動(dòng) 時(shí)間: 2025-3-26 11:55 作者: reaching 時(shí)間: 2025-3-26 12:58
,L’équivalence duale de catégories: ,?,t. Its main benefit lies in the fact that it allows us to convert bilinear mappings into homomorphisms of abelian groups. The relations between tensor products and homomorphism groups is fundamental and will lead us to the concept of adjoint functor in the later part of the chapter.作者: hyperuricemia 時(shí)間: 2025-3-26 18:52
,Analysis and Synthesis in Robert Simson’s ,g .[.] is semisimple, provided . is a finite group. For any field ., the elements of . form a basis of the .-vector space .[.] and if the ring .[.] is semisimple, then it is necessarily Artinian, hence finite dimensional (Corollary . and Exercise .). As a result, we cannot expect .[.] to be semisimple for an infinite group ..作者: alleviate 時(shí)間: 2025-3-26 23:25
Motivation from Ring Theory,stances where the setting of Ring Theory in its strictest sense turns out to be too narrow, or at least somewhat cumbersome, in order to provide us with enough tools for studying certain properties of rings. We shall take this as part of our motivation to introduce the more comprehensive setting of modules below.作者: BUDGE 時(shí)間: 2025-3-27 02:56 作者: palliative-care 時(shí)間: 2025-3-27 05:53 作者: cortex 時(shí)間: 2025-3-27 11:47
Semiprimitivity of Group Rings,g .[.] is semisimple, provided . is a finite group. For any field ., the elements of . form a basis of the .-vector space .[.] and if the ring .[.] is semisimple, then it is necessarily Artinian, hence finite dimensional (Corollary . and Exercise .). As a result, we cannot expect .[.] to be semisimple for an infinite group ..作者: 不怕任性 時(shí)間: 2025-3-27 16:03 作者: 關(guān)節(jié)炎 時(shí)間: 2025-3-27 21:31 作者: athlete’s-foot 時(shí)間: 2025-3-28 01:33
d biographical sketches of important figures scattered throughout the text..Assuming previous knowledge in linear and basic abstract algebra, this book can serve as a textbook for a course in algebra, providing students with valuable early exposure to category theory..978-3-031-14208-6978-3-031-14209-3作者: 輕率的你 時(shí)間: 2025-3-28 02:17 作者: 秘傳 時(shí)間: 2025-3-28 08:40
9樓作者: Custodian 時(shí)間: 2025-3-28 11:04
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