21:
17:
35:
Bezout's lemma can be proved as a corollary of the proof that the integers are a PID.
47:
M is a set of numbers closed under addition and subtraction. In symbols, if
99:
Lemma: If M is a nonzero ideal it contains a postiive number. Proof: let
91:
Definition: A ideal that contains a number other than 0 is called a
205:
Actually, it is sufficient that it be closed under subtraction.
194:
Prime
Numbers and Computer Methods in Factorization
8:
119:Lemma: The set of all multiples of a number
83:Definition: The set M = {0} is called the
67:Lemma: If M is a ideal, 0 ∈ M. Proof: let
185:
7:
192:This proof is based on Hans Riesel,
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139:,...} is an ideal. Proof: Let
1:
223:
18:User:Virginia-American
111:> 0 or M ∋ 0 −
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206:
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197:
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118:
98:
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82:
66:
41:
33:
26:
25:
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12:
11:
5:
220:
218:
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184:
183:
123:, M = {..., −2
43:Definition: A
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116:
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96:
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93:nonzero ideal
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38:
36:
30:
23:
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196:, appendix 1
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136:
132:
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107:≠ 0. Either
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84:
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72:
68:
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34:
155:∈ M. Then
85:zero ideal
71:∈ M. Then
79:= 0 ∈ M.
55:∈ M then
115:> 0.
20: |
39:Modules
22:Sandbox
175:∈ M.
131:, 0,
103:∈ M,
63:∈ M.
45:ideal
31:Proof
16:<
163:= (
135:, 2
127:, −
87:.
167:±
159:±
153:nd
151:=
147:,
145:md
143:=
95:.
75:−
59:±
51:,
173:d
171:)
169:n
165:m
161:b
157:a
149:b
141:a
137:d
133:d
129:d
125:d
121:d
113:a
109:a
105:a
101:a
77:a
73:a
69:a
61:b
57:a
53:b
49:a
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