harbinger 发表于 2025-3-26 22:20:14
Groups,.. is a set, together with a rule (called a .) which to each pair of elements ., . in . associates an element denoted by . in ., having the following properties.津贴 发表于 2025-3-27 04:42:53
Rings,In this chapter, we axiomatize the notions of addition and multiplication.Diverticulitis 发表于 2025-3-27 06:32:12
Polynomials,Let . be a field. Every reader of this book will have written expressions like . where ..,...,.. are real or complex numbers. We could also take these to be elements of .. But what does “.” mean? Or powers of “.” like ., ..,...,..?欢乐中国 发表于 2025-3-27 09:57:49
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Field Theory,Let . be a subfield of a field .. We also say that . is an . of . and we denote the extension by .. Let . be a field. An element α in some extension of . is said to be . over . if there exists a non-zero polynomial .[.]such that .(α) = 0, i.e. if α satisfies a polynomial equationfigurine 发表于 2025-3-27 18:47:27
The Real and Complex Numbers,Let . be an integral ring. By an . of . one means a subset . of . satisfying the following conditions:Sad570 发表于 2025-3-27 22:17:12
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