Элементы абстрактной и компьютерной алгебры. Учебное пособие
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§1. НЕОБХОДИМЫЕ СВЕДЕНИЯ ИЗ АБСТРАКТНОЙ АЛГЕБРЫ
xɆɧɨɠɟɫɬɜɨ ɰɟɥɵɯ ɱɢɫɟɥ ɨɬɧɨɫɢɬɟɥɶɧɨ ɨɩɟɪɚɰɢɣ ɫɥɨɠɟɧɢɹ ɢ ɭɦɧɨɠɟ ɧɢɹ ɹɜɥɹɟɬɫɹ ɤɨɥɶɰɨɦ
xɆɧɨɠɟɫɬɜɨ ɜɫɟɯ ɤɜɚɞɪɚɬɧɵɯ ɦɚɬɪɢɰ ɪɚɡɦɟɪɚ F ɰɟɥɵɦɢ ɷɥɟ ɦɟɧɬɚɦɢ ɹɜɥɹɟɬɫɹ ɤɨɥɶɰɨɦ ɨɬɧɨɫɢɬɟɥɶɧɨ ɨɩɟɪɚɰɢɣ ɫɥɨɠɟɧɢɹ ɢ ɭɦɧɨɠɟ ɧɢɹ ɦɚɬɪɢɰ
xɆɧɨɠɟɫɬɜɨݔɦɧɨɝɨɱɥɟɧɨɜ ɫ ɰɟɥɨɱɢɫɥɟɧɧɵɦɢ ɤɨɷɮɮɢɰɢɟɧɬɚɦɢ ɹɜ ɥɹɟɬɫɹ ɤɨɥɶɰɨɦ ɨɬɧɨɫɢɬɟɥɶɧɨ ɨɩɟɪɚɰɢɣ ɫɥɨɠɟɧɢɹ ɢ ɭɦɧɨɠɟɧɢɹ ɦɧɨɝɨ ɱɥɟɧɨɜ
ȿɫɥɢ ɞɥɹ ɤɨɥɶɰɚۃ ǡ ǡήۄɞɨɩɨɥɧɢɬɟɥɶɧɨ ɜɵɩɨɥɧɹɟɬɫɹ ɭɫɥɨɜɢɟɤɨɦɦɭɬɚɬɢɜɧɨ
ɫɬɢ ɭɦɧɨɠɟɧɢɹ
ɞɥɹ ɥɸɛɵɯ ɷɥɟɦɟɧɬɨɜǡ א
ɬɨ ɤɨɥɶɰɨ ɧɚɡɵɜɚɟɬɫɹɤɨɦɦɭɬɚɬɢɜɧɵɦ
Ʉɪɨɦɟ ɬɨɝɨ ɟɫɥɢ ɜ ɞɨɩɨɥɧɟɧɢɟ ɤ ɫɜɨɣɫɬɜɚɦ ± ɜɵɩɨɥɧɹɟɬɫɹ ɭɫɥɨɜɢɟ
ɞɥɹ ɥɸɛɨɝɨ ɧɟɧɭɥɟɜɨɝɨ ɷɥɟɦɟɧɬɚ ɤɨɥɶɰɚɫɭɳɟɫɬɜɭɟɬ ɨɛɪɚɬɧɵɣ
ɷɥɟɦɟɧɬ א ɞɥɹ ɤɨɬɨɪɨɝɨ ή ɬɨ ɤɨɥɶɰɨ ɧɚɡɵɜɚɟɬɫɹɩɨɥɟɦ
ɉɪɢɦɟɪɵ
xɆɧɨɠɟɫɬɜɨ ɰɟɥɵɯ ɱɢɫɟɥ ɨɬɧɨɫɢɬɟɥɶɧɨ ɨɩɟɪɚɰɢɣ ɫɥɨɠɟɧɢɹ ɢ ɭɦɧɨɠɟ ɧɢɹ ɹɜɥɹɟɬɫɹ ɤɨɥɶɰɨɦ ɧɨ ɧɟ ɹɜɥɹɟɬɫɹ ɩɨɥɟɦ ɋɜɨɣɫɬɜɨ ɧɟ ɜɵɩɨɥɧɟɧɨ ɞɥɹ ɷɥɟɦɟɧɬɨɜ ɨɬɥɢɱɧɵɯ ɨɬ ɢ
xɆɧɨɠɟɫɬɜɚǡ ǡɪɚɰɢɨɧɚɥɶɧɵɯ ɞɟɣɫɬɜɢɬɟɥɶɧɵɯ ɢ ɤɨɦɩɥɟɤɫɧɵɯ ɱɢ ɫɟɥ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ ɨɬɧɨɫɢɬɟɥɶɧɨ ɨɩɟɪɚɰɢɣ ɫɥɨɠɟɧɢɹ ɢ ɭɦɧɨɠɟɧɢɹ ɨɛɪɚ ɡɭɸɬ ɩɨɥɟ
x Ⱥɥɝɟɛɪɚɢɱɟɫɤɢɟ ɱɢɫɥɨɜɵɟ ɩɨɥɹξʹ ξ͵ ɹɜɥɹɸɬɫɹ ɩɨɥɹɦɢ
x Ʉɨɧɟɱɧɵɟ ɩɨɥɹ Ʉɨɥɶɰɚ ɜɵɱɟɬɨɜ ɨɛɪɚɡɭɸɬ ɩɨɥɟ ɬɨɝɞɚ ɢ ɬɨɥɶɤɨ ɬɨɝɞɚ
ɤɨɝɞɚ ± ɩɪɨɫɬɨɟ ɱɢɫɥɨ ɇɚɩɪɢɦɟɪ ± ɩɨɥɟ ɚ ± ɧɟ ɩɨɥɟ
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А.В.Царев,Г.В.Шеина. ЭЛЕМЕНТЫ АБСТРАКТНОЙ И КОМПЬЮТЕРНОЙ АЛГЕБРЫ
Ɉɫɨɛɵɣ ɤɥɚɫɫ ɤɨɥɟɰ ɨɛɪɚɡɭɸɬ ɤɨɥɶɰɚ ɛɟɡ ɞɟɥɢɬɟɥɟɣ ɧɭɥɹ
Ɉɩɪɟɞɟɥɟɧɢɟ ɇɟɧɭɥɟɜɨɣɷɥɟɦɟɧɬ א ɧɚɡɵɜɚɟɬɫɹɞɟɥɢɬɟɥɟɦ ɧɭɥɹɟɫɥɢ ɫɭ
ɳɟɫɬɜɭɟɬɧɟɧɭɥɟɜɨɣɷɥɟɦɟɧɬ א ɞɥɹ ɤɨɬɨɪɨɝɨ ɗɥɟɦɟɧɬ ɬɚɤɠɟ
ɧɚɡɵɜɚɟɬɫɹ ɞɟɥɢɬɟɥɟɦ ɧɭɥɹ
ɈɩɪɟɞɟɥɟɧɢɟɄɨɥɶɰɨۃ ǡ ǡήۄɧɚɡɵɜɚɟɬɫɹɨɛɥɚɫɬɶɸ ɰɟɥɨɫɬɧɨɫɬɢɟɫɥɢ ±
ɤɨɦɦɭɬɚɬɢɜɧɨɟ ɤɨɥɶɰɨ ɛɟɡ ɞɟɥɢɬɟɥɟɣ ɧɭɥɹ Ɉɛɥɚɫɬɢ ɰɟɥɨɫɬɧɨɫɬɢ ɧɚɡɵɜɚɸɬ
ɬɚɤɠɟɰɟɥɵɦɢ ɤɨɥɶɰɚɦɢ
ɉɪɢɦɟɪɵ
xɑɢɫɥɨɜɵɟ ɤɨɥɶɰɚ ɬɨ ɟɫɬɶ ɩɨɞɤɨɥɶɰɚ ɩɨɥɹ ɤɨɦɩɥɟɤɫɧɵɯ ɱɢɫɟɥ ɧɟ ɢɦɟɸɬ ɞɟ
ɥɢɬɟɥɟɣ ɧɭɥɹ ɢ ɩɨɷɬɨɦɭ ɹɜɥɹɸɬɫɹ ɰɟɥɵɦɢ ɤɨɥɶɰɚɦɢ ȼ ɱɚɫɬɧɨɫɬɢ ɤɨɥɶɰɨ ɰɟ
ɥɵɯ ɱɢɫɟɥ ɬɚɤɠɟ ɟɫɬɶ ɰɟɥɨɟ ɤɨɥɶɰɨ ɞɚɜɲɟɟ ɧɚɡɜɚɧɢɟ ɷɬɨɦɭ ɤɥɚɫɫɭ ɤɨɥɟɰ
xɄɨɥɶɰɨ ɜɵɱɟɬɨɜ ɧɟ ɹɜɥɹɟɬɫɹ ɰɟɥɵɦ ɤɨɥɶɰɨɦ ɩɨɫɤɨɥɶɤɭ ɜ ɧɟɦ ɷɥɟɦɟɧɬʹ ɹɜɥɹɟɬɫɹ ɞɟɥɢɬɟɥɟɦ ɧɭɥɹʹ ή ʹ
xɄɨɥɶɰɨ ɧɟ ɹɜɥɹɟɬɫɹ ɰɟɥɵɦ ɤɨɥɶɰɨɦ ɩɨɫɤɨɥɶɤɭ ɨɧɨ ɧɟ ɤɨɦɦɭɬɚɬɢɜɧɨ
ɢ ɢɦɟɟɬ ɞɟɥɢɬɟɥɢ ɧɭɥɹ |
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x Ʉɨɥɶɰɨ ɞɜɨɣɧɵɯ ɱɢɫɟɥ ɱɢɫɟɥ ɜɢɞɚ ɝɞɟ ± ɧɟɞɟɣɫɬɜɢɬɟɥɶɧɨɟ
ɱɢɫɥɨ ɤɜɚɞɪɚɬ ɤɨɬɨɪɨɝɨ ɪɚɜɟɧ ɟɞɢɧɢɰɟ
Ɇɚɬɪɢɱɧɚɹ ɪɟɚɥɢɡɚɰɢɹ |
ȼ ɷɬɨɦ ɤɨɥɶɰɟ |
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xɅɸɛɨɟ ɩɨɥɟ ɟɫɬɶ ɰɟɥɨɟ ɤɨɥɶɰɨ ɞɨɤɚɠɢɬɟ ɷɬɨ
xȿɫɥɢ ± ɰɟɥɨɟ ɤɨɥɶɰɨ ɬɨݔ± ɬɚɤɠɟ ɰɟɥɨɟ ɤɨɥɶɰɨ
ɁɚɞɚɱɚɈɛɪɚɡɭɸɬ ɥɢ ɤɨɥɶɰɨ ɦɧɨɠɟɫɬɜɨ ɱɢɫɟɥ ɜɢɞɚ ξʹɝɞɟξʹ± ɞɟɣɫɬɜɢ
ɬɟɥɶɧɵɣ ɤɨɪɟɧɶ ɢɡ ɞɜɭɯ ɫ ɪɚɰɢɨɧɚɥɶɧɵɦɢ ɤɨɷɮɮɢɰɢɟɧɬɚɦɢ ɢ ɨɬɧɨɫɢɬɟɥɶɧɨ
ɫɥɨɠɟɧɢɹ ɢ ɭɦɧɨɠɟɧɢɹ ɞɟɣɫɬɜɢɬɟɥɶɧɵɯ ɱɢɫɟɥ"
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§1. НЕОБХОДИМЫЕ СВЕДЕНИЯ ИЗ АБСТРАКТНОЙ АЛГЕБРЫ
ɊɟɲɟɧɢɟɊɚɫɫɦɨɬɪɢɦ ɱɢɫɥɨ ξʹ ξɉɨɤɚɠɟɦ ɱɬɨ ɨɧɨ ɧɟ ɹɜɥɹɟɬɫɹ ɱɢɫɥɨɦ
ɜɢɞɚ ξʹ ǡ א Ⱦɟɣɫɬɜɢɬɟɥɶɧɨ ɟɫɥɢξ ξʹɬɨ ɜɨɡɜɟɞɹ ɪɚɜɟɧ
ɫɬɜɨ ɜ ɤɜɚɞɪɚɬ ɩɨɥɭɱɢɦʹξʹ ʹξʹ ξɁɧɚɱɢɬ
ξ ʹ ʹξʹ Ǥ
ɉɨɞɫɬɚɜɢɦξ ξʹɜ ɩɨɫɥɟɞɧɟɟ ɪɚɜɟɧɫɬɜɨ ɩɟɪɟɧɟɫɟɦ ɫɥɚɝɚɟɦɵɟ ɫ ɤɨɪɧɟɦ
ɜ ɥɟɜɭɸ ɱɚɫɬɶ ɪɚɜɟɧɫɬɜɚ ɚ ɨɫɬɚɥɶɧɵɟ ɜ ɩɪɚɜɭɸ ɱɚɫɬɶ ɢ ɩɨɥɭɱɢɦ
ʹ ʹ ξʹ
Ɉɬɫɸɞɚ ɫɥɟɞɭɟɬ ɱɬɨ
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ɬɨ ɟɫɬɶ ɱɢɫɥɨ |
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ɧɚɥɶɧɨɟ ɱɢɫɥɨ ɚ ɷɬɨ ɧɟ ɬɚɤ |
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ɟɫɥɢʹ ʹ ɬɨ ɢ ɦɵ ɢɦɟɟɦ |
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ɉɪɨɜɟɪɢɦ ɱɬɨ ɨɧɚ ɧɟ ɢɦɟɟɬ ɪɟɲɟɧɢɣ ɜ ɪɚɰɢɨɧɚɥɶɧɵɯ ɱɢɫɥɚɯ Ⱦɟɣɫɬɜɢɬɟɥɶɧɨ ɢɡ
ɜɬɨɪɨɝɨ ɭɪɚɜɧɟɧɢɹ ɫɥɟɞɭɟɬ ɱɬɨ ɢɥɢ ȼ ɫɥɭɱɚɟ ɩɪɢɯɨɞɢɦ
ɤ ɭɪɚɜɧɟɧɢɸ ʹɜ ɫɥɭɱɚɟ ɩɪɢɯɨɞɢɦ ɤ ɭɪɚɜɧɟɧɢɸ ʹɈɛɚ
ɭɪɚɜɧɟɧɢɹ ɧɟ ɢɦɟɸɬ ɪɟɲɟɧɢɣ ɜ ɪɚɰɢɨɧɚɥɶɧɵɯ ɱɢɫɥɚɯ
Ɉɬɜɟɬɱɢɫɥɚ ɭɤɚɡɚɧɧɨɝɨ ɜɢɞɚ ɧɟ ɨɛɪɚɡɭɸɬ ɤɨɥɶɰɨ
ȼɵɱɢɫɥɟɧɢɟ ɨɛɪɚɬɧɨɣ ɦɚɬɪɢɰɵ
ɉɪɢɦɟɪɨɦ ɧɟɤɨɦɦɭɬɚɬɢɜɧɨɝɨ ɤɨɥɶɰɚ ɹɜɥɹɟɬɫɹ ɤɨɥɶɰɨ ɦɚɬɪɢɰ ȼ ɧɟɤɨɦɦɭɬɚɬɢɜ
ɧɨɦ ɤɨɥɶɰɟ ɭɪɚɜɧɟɧɢɹݔ ɢݔ ɦɨɝɭɬ ɢɦɟɬɶ ɪɚɡɧɵɟ ɪɟɲɟɧɢɹ Ʉɪɨɦɟ
ɬɨɝɨ ɢɦɟɟɬɫɹ ɟɳɟ ɬɪɟɬɢɣ ɬɢɩ ɭɪɚɜɧɟɧɢɣݔ Ɉɫɬɚɧɨɜɢɦɫɹ ɩɨɞɪɨɛɧɟɟ ɧɚ
ɪɟɲɟɧɢɢ ɬɚɤɢɯ ɦɚɬɪɢɱɧɵɯ ɭɪɚɜɧɟɧɢɣ ɋɧɚɱɚɥɚ ɧɚɭɱɢɦɫɹ ɜɵɱɢɫɥɹɬɶ ɨɛɪɚɬɧɭɸ
ɦɚɬɪɢɰɭ
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А.В.Царев,Г.В.Шеина. ЭЛЕМЕНТЫ АБСТРАКТНОЙ И КОМПЬЮТЕРНОЙ АЛГЕБРЫ
Ɉɛɪɚɬɧɚɹ ɦɚɬɪɢɰɚ ɜɵɱɢɫɥɹɟɬɫɹ ɦɟɬɨɞɨɦ Ƚɚɭɫɫɚ Ɉɩɢɲɟɦ ɚɥɝɨɪɢɬɦ ɜɵɱɢɫɥɟɧɢɹ ɉɭɫɬɶ ɞɥɹ ɦɚɬɪɢɰɵ ɬɪɟɛɭɟɬɫɹ ɧɚɣɬɢ ɨɛɪɚɬɧɭɸ ɦɚɬɪɢɰɭ ɗɬɨ ɨɡɧɚɱɚɟɬ ɱɬɨ ɦɵ ɞɨɥɠɧɵ ɪɟɲɢɬɶ ɨɞɧɨɜɪɟɦɟɧɧɨ ɧɟɫɤɨɥɶɤɨ ɫɢɫɬɟɦ ɭɪɚɜɧɟɧɢɣ ɨɫɧɨɜɧɨɣ ɦɚɬɪɢɰɟɣ ɤɨɬɨɪɵɯ ɹɜɥɹɟɬɫɹ ɦɚɬɪɢɰɚ
Ɉɛɨɡɧɚɱɢɦ ɩɟɪɜɵɣ ɫɬɨɥɛɟɰ ɤɜɚɞɪɚɬɧɨɣ ɦɚɬɪɢɰɵ ɪɚɡɦɟɪɚ ɬɚɤ |
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ȿɫɥɢ ± ɨɛɪɚɬɧɚɹ ɦɚɬɪɢɰɚ ɬɨ ɦɵ ɞɨɥɠɧɵ ɪɟɲɢɬɶ ɫɢɫɬɟɦɵ ɭɪɚɜɧɟɧɢɣ
ή ǡ ڭ ǡǥǡ ήǡ ڭǤ
ɉɨ ɞɪɭɝɨɦɭ ɡɚɩɢɫɵɜɚɟɦ ɟɞɢɧɢɱɧɭɸ ɦɚɬɪɢɰɭ ɫɩɪɚɜɚ ɨɬ ɦɚɬɪɢɰɵ ɢ ɩɪɢɜɨɞɢɦ
ɥɟɜɭɸ ɦɚɬɪɢɰɭ ɤ ɟɞɢɧɢɱɧɨɣ ɦɚɬɪɢɰɟ Ɍɨɝɞɚ ɧɚ ɦɟɫɬɟ ɩɪɚɜɨɣ ɦɚɬɪɢɰɵ ɛɭɞɟɬ
ɧɚɯɨɞɢɬɶɫɹ ɨɛɪɚɬɧɚɹ ɦɚɬɪɢɰɚ $ |
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24
§1. НЕОБХОДИМЫЕ СВЕДЕНИЯ ИЗ АБСТРАКТНОЙ АЛГЕБРЫ
Ɋɟɲɟɧɢɟ ɦɚɬɪɢɱɧɵɯ ɭɪɚɜɧɟɧɢɣ
, ɂɫɩɨɥɶɡɭɟɦ ɪɚɡɨɛɪɚɧɧɵɣ ɩɪɢɟɦ ɜ ɫɥɭɱɚɟ ɤɨɝɞɚ ɦɚɬɪɢɰɚ ɨɛɪɚɬɢɦɚ
ɢ ɧɭɠɧɨ ɪɟɲɢɬɶ ɦɚɬɪɢɱɧɨɟ ɭɪɚɜɧɟɧɢɟ ɜɢɞɚ
ɋɯɟɦɚ ɪɟɲɟɧɢɹ ɬɚ ɠɟ$ % ɦɟɬɨɞ Ƚɚɭɫɫɚo( ;
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,, ɍɪɚɜɧɟɧɢɹ ɬɢɩɚ ɦɨɠɧɨ ɪɟɲɚɬɶ ɞɜɭɦɹ ɫɩɨɫɨɛɚɦɢ
ɋɩɨɫɨɛ ɩɟɪɜɵɣ Ɍɪɚɧɫɩɨɧɢɪɨɜɚɬɶ ɦɚɬɪɢɱɧɨɟ ɪɚɜɟɧɫɬɜɨ ɩɨɥɭɱɢɬɶ ɧɨ
ɜɨɟ ɭɪɚɜɧɟɧɢɟ Ⱦɚɥɟɟ ɪɟɲɚɬɶ ɩɨ ɩɪɟɞɵɞɭɳɟɣ ɫɯɟɦɟ ɧɚɯɨɞɹ ɫɧɚɱɚɥɚ
ɬɪɚɧɫɩɨɧɢɪɨɜɚɧɧɭɸ ɦɚɬɪɢɰɭ $7 %7 ɦɟɬɨɞ Ƚɚɭɫɫɚo;7 (
ɋɩɨɫɨɛ ɜɬɨɪɨɣ ֜
ɁɚɞɚɱɚɊɟɲɢɬɟ ɞɜɭɦɹ ɫɩɨɫɨɛɚɦɢ ɦɚɬɪɢɱɧɨɟ ɭɪɚɜɧɟɧɢɟ
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25
А.В.Царев,Г.В.Шеина. ЭЛЕМЕНТЫ АБСТРАКТНОЙ И КОМПЬЮТЕРНОЙ АЛГЕБРЫ
,,, ɂɦɟɟɬɫɹ ɟɳɟ ɬɪɟɬɢɣ ɫɥɭɱɚɣ ɭɪɚɜɧɟɧɢɹ ɜɢɞɚ ȼ ɫɥɭɱɚɟ ɨɛɪɚɬɢɦɨ
ɫɬɢ ɦɚɬɪɢɰ ɢ ɪɟɲɟɧɢɟ ɦɨɠɧɨ ɧɚɯɨɞɢɬɶ ɩɨ ɮɨɪɦɭɥɟ Ǥ
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ȼɚɪɢɚɧɬɵ ɞɥɹ ɫɚɦɨɫɬɨɹɬɟɥɶɧɵɯ ɪɚɛɨɬ
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ɇɚɣɞɢɬɟ ɨɛɪɚɬɧɭɸ ɦɚɬɪɢɰɭ ɞɥɹ ɦɚɬɪɢɰɵ $ |
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26
§1. НЕОБХОДИМЫЕ СВЕДЕНИЯ ИЗ АБСТРАКТНОЙ АЛГЕБРЫ
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27
А.В.Царев,Г.В.Шеина. ЭЛЕМЕНТЫ АБСТРАКТНОЙ И КОМПЬЮТЕРНОЙ АЛГЕБРЫ
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28
§1. НЕОБХОДИМЫЕ СВЕДЕНИЯ ИЗ АБСТРАКТНОЙ АЛГЕБРЫ
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Ɍɟɨɪɢɹ ɞɟɥɢɦɨɫɬɢ ɜ ɤɨɦɦɭɬɚɬɢɜɧɵɯ ɤɨɥɶɰɚɯ
ɈɩɪɟɞɟɥɟɧɢɟȽɨɜɨɪɹɬ ɱɬɨ ɷɥɟɦɟɧɬ ɢɡ ɤɨɦɦɭɬɚɬɢɜɧɨɝɨ ɤɨɥɶɰɚ ɞɟɥɢɬɷɥɟ
ɦɟɧɬ א ɢɥɢ ɞɟɥɢɬɫɹ ɧɚ ɷɥɟɦɟɧɬ ɟɫɥɢ ɫɭɳɟɫɬɜɭɟɬ ɷɥɟɦɟɧɬ א ɞɥɹ
ɤɨɬɨɪɨɝɨ
ɈɩɪɟɞɟɥɟɧɢɟȽɨɜɨɪɹɬ ɱɬɨ ɷɥɟɦɟɧɬɵ ɢ ɤɨɥɶɰɚ ɚɫɫɨɰɢɢɪɨɜɚɧɵɟɫɥɢ ɨɧɢ
ɞɟɥɹɬ ɞɪɭɝ ɞɪɭɝɚ
Ȼɭɞɟɦ ɢɫɩɨɥɶɡɨɜɚɬɶ ɫɥɟɞɭɸɳɢɟ ɨɛɨɡɧɚɱɟɧɢɹ
ɷɥɟɦɟɧɬ ɞɟɥɢɬɫɹ
ڭ
ɧɚ ɷɥɟɦɟɧɬ
ȁ ɞɟɥɢɬ
ɷɥɟɦɟɧɬɵ ɢ
̱
ɚɫɫɨɰɢɢɪɨɜɚɧɵ
ɉɪɢɦɟɪɵ
xȿɫɥɢ ɬɨ ɞɥɹ ɥɸɛɨɝɨ ɷɥɟɦɟɧɬɚ א ɢɦɟɟɦȁɢȁȿɫɥɢȁ ɬɨ
xȿɫɥɢ ɬɨʹȁ͵
29
А.В.Царев,Г.В.Шеина. ЭЛЕМЕНТЫ АБСТРАКТНОЙ И КОМПЬЮТЕРНОЙ АЛГЕБРЫ
xȿɫɥɢ ± ɨɛɥɚɫɬɶ ɰɟɥɨɫɬɧɨɫɬɢ ɬɨ̱ ֞ ɝɞɟ ± ɨɛɪɚɬɢɦɵɣ ɷɥɟɦɟɧɬ ɤɨɥɶɰɚ
xȼ ɤɨɥɶɰɟ ɨɛɪɚɬɢɦɵ ɬɨɥɶɤɨ ɷɥɟɦɟɧɬɵ Ʉɪɨɦɟ ɬɨɝɨ̱ ֞
xȿɫɥɢ ± ɩɨɥɟ ɬɨ ɜ ɤɨɥɶɰɟ ɦɧɨɝɨɱɥɟɧɨɜݔɨɛɪɚɬɢɦɵ ɬɨɥɶɤɨ ɦɧɨɝɨ ɱɥɟɧɵ ɧɭɥɟɜɨɣ ɫɬɟɩɟɧɢ ɨɬɥɢɱɧɵɟ ɨɬ ɧɭɥɟɜɨɝɨ ɦɧɨɝɨɱɥɟɧɚ
xȼ ɤɨɥɶɰɟ ɦɧɨɝɨɱɥɟɧɨɜݔɦɧɨɝɨɱɥɟɧɵݔ ɢʹݔ ʹɚɫɫɨɰɢɢɪɨɜɚɧɵ ɚ ɦɧɨɝɨɱɥɟɧɵݔ ɢʹݔ ɚɫɫɨɰɢɢɪɨɜɚɧɧɵɦɢ ɧɟ ɹɜɥɹɸɬɫɹ
30