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pineapple.cc ܈ɾ؀ɾମgroup, ring, field

pineapple.cc ܈ͱ൒܈ Group and Semigroup w ดੑ w ݁߹ੑ w தཱݩͷଘࡏ w ٯݩͷଘࡏʢ܈ͷΈʣ {੔਺} + {੔਺} = {੔਺} (A + B) + C = A + (B + C) 0 + A = A + 0 = A (−A) + A = A + (−A) = 0

pineapple.cc ܈ͱ൒܈ º Group and Semigroup w ดੑ w ݁߹ੑ w தཱݩͷଘࡏ w ٯݩͷଘࡏʢ܈ͷΈʣ {੔਺} × {੔਺} = {੔਺} (A × B) × C = A × (B × C) 1 × A = A × 1 = A A−1 × A = A × A−1 = 1 (A ≠ 0)

pineapple.cc ؀ º Ring w ดੑʢՃ๏ͱ৐๏ʣ w ݁߹ੑʢՃ๏ͱ৐๏ʣ w தཱݩͷଘࡏʢՃ๏ͱ৐๏ʣ w ٯݩͷଘࡏʢՃ๏ʣ w Մ׵ੑʢՃ๏ʣ w ෼഑ੑ {੔਺} + {੔਺} = {੔਺}, {੔਺} × {੔਺} = {੔਺} (A + B) + C = A + (B + C), (A × B) × C = A × (B × C) 0 + A = A + 0 = A, 1 × A = A × 1 = A (−A) + A = A + (−A) = 0, A−1 × A = A × A−1 = 1 (A ≠ 0) A + B = B + A A × (B + C) = A × B + A × C

pineapple.cc A B A B

pineapple.cc ϒʔϧ୅਺ͱਐ๏ͷ੔਺୅਺ Boolean Algebra and Integral Algebra of Binary System w ϒʔϧ୅਺ w ˔PS˔˔ w ˔PS̋̋ w ̋PS˔̋ w ̋PS̋̋ w ਐ๏ͷ੔਺୅਺ w w w w

pineapple.cc ϒʔϧ୅਺ͱਐ๏ͷ੔਺୅਺ Boolean Algebra and Integral Algebra of Binary System w ϒʔϧ୅਺ w ˔BOE˔˔ w ˔BOE̋˔ w ̋BOE˔˔ w ̋BOE̋̋ w ਐ๏ͷ੔਺୅਺ w Y w Y w Y w Y

pineapple.cc ϒʔϧ୅਺ͱਐ๏ͷ੔਺୅਺ Boolean Algebra and Integral Algebra of Binary System w ϒʔϧ୅਺ w OPU˔̋ w OPŰ˔ w OPU "PS# OPU" BOE OPU# XIFSF" #㱨\˔ ̋^ w OPU "BOE# OPU" PS OPU# XIFSF" #㱨\˔ ̋^

pineapple.cc ϒʔϧ୅਺ͱਐ๏ͷ੔਺୅਺ Boolean Algebra and Integral Algebra of Binary System w ࿦ཧ୅਺ͱϒʔϧ୅਺ w w w w ܭࢉػՊֶͰ͸ਐ๏ͷ੔਺୅਺Λࢉज़ʢBSJUINFUJDʣૢ࡞ɼϒʔϧ୅਺Λ ࿦ཧʢMPHJDBMʣૢ࡞ͱݺͿ ¯ A ≜ OPU A A ∩ B ≜ A BOE B A ∪ B ≜ A PS B

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