Download Algebra Volume 2, 2nd Edition by P. M. Cohn PDF

By P. M. Cohn

The most emphasis of this revised algebra textbook is on fields, jewelry and modules. The textual content comprises new chapters at the consultant idea of finite teams, coding concept and algebraic language conception. units, lattices, different types and graphs are brought first and foremost of the textual content. The textual content, which has been rewritten with the purpose of constructing the topic more straightforward to know, comprises simplified proofs and plenty of new illustrations and routines.

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T✐♣❧② t❤❡ ❢r❛❝t✐♦♥s. 60% ❘❡♣❧❛❝❡ 1 100 ✇✐t❤ t❤❡ % s②♠❜♦❧. 75 ✐s ❝♦♥✈❡rt❡❞ t♦ ❛ 1 100 . 75 · 100 · = 75 · = 75% 1 100 ▼✉❧t✐♣❧② t❤❡ ❞❡❝✐♠❛❧ ❜② ✶✳ 1 100 ❘❡♣❧❛❝❡ 1 100 ✇✐t❤ t❤❡ ✪ s②♠❜♦❧. 623% 1 100 1 100 ◆♦t✐❝❡ t❤❛t t❤❡ ❞❡❝✐♠❛❧ ♣♦✐♥t ✐♥ t❤❡ ♦r✐❣✐♥❛❧ ♥✉♠❜❡r ❤❛s ❜❡❡♥ ♠♦✈❡❞ t♦ t❤❡ r✐❣❤t ✷ ♣❧❛❝❡s✳ ✶✳✽✳✼ ❈♦♥✈❡rt✐♥❣ ❆ P❡r❝❡♥t ❚♦ ❆ ❉❡❝✐♠❛❧ ❲❡ ❝❛♥ s❡❡ ❤♦✇ ❛ ♣❡r❝❡♥t ✐s ❝♦♥✈❡rt❡❞ t♦ ❛ ❞❡❝✐♠❛❧ ❜② ❛♥❛❧②③✐♥❣ t❤❡ ♠❡t❤♦❞ t❤❛t ✶✷✪ ✐s ❝♦♥✈❡rt❡❞ t♦ ❛ ❞❡❝✐♠❛❧✳ ❲❡ ♥❡❡❞ t♦ ✐♥tr♦❞✉❝❡ 1 100 . 12% 1 100 1 100 . = 12 · = 12 100 ▼✉❧t✐♣❧② t❤❡ ❢r❛❝t✐♦♥s.

S t❤❡ ♦♥❧② ❝♦♠♠♦♥ ❢❛❝t♦r. ◆♦t✐❝❡ t❤❛t ✇❡ s✐♥❝❡ ❤❛❞ t♦ r❡❞✉❝❡✱ ✇❡ ♥❡❛r❧② st❛rt❡❞ ♦✈❡r ❛❣❛✐♥ ✇✐t❤ t❤❡ ♦r✐❣✐♥❛❧ t✇♦ ❢r❛❝t✐♦♥s✳ ■❢ ✇❡ ❢❛❝t♦r ✜rst✱ t❤❡♥ ❝❛♥❝❡❧✱ t❤❡♥ ♠✉❧t✐♣❧②✱ ✇❡ ✇✐❧❧ s❛✈❡ t✐♠❡ ❛♥❞ ❡♥❡r❣② ❛♥❞ st✐❧❧ ♦❜t❛✐♥ t❤❡ ❝♦rr❡❝t ♣r♦❞✉❝t✳ ✶✳✻✳✸ ❙❛♠♣❧❡ ❙❡t ❆ P❡r❢♦r♠ t❤❡ ❢♦❧❧♦✇✐♥❣ ♠✉❧t✐♣❧✐❝❛t✐♦♥s✳ ❊①❛♠♣❧❡ ✶✳✷✺ 1 4 · 8 9 = = = = = 1 2·2·2 2·2 · 3·3 ·2 1 · )2 3· )2 ·3 )2 · )2 2 1 1 · 3·3 1·2 1·3·3 2 9 ✷ ✐s ❛ ❝♦♠♠♦♥ ❢❛❝t♦r✳ ❊①❛♠♣❧❡ ✶✳✷✻ 3 4 · 8 9 · 5 12 = = = = 3 2·2·2 5 2·2 · 3·3 · 2·2·3 )3 5 · )2 · )2 · )2 · )2 · )2 )3 · 3 )2 · 2 · 3 1·1·5 3·2·3 5 18 ✷ ❛♥❞ ✸ ❛r❡ ❝♦♠♠♦♥ ❢❛❝t♦rs✳ ✶✳✻✳✹ ❉✐✈✐s✐♦♥ ♦❢ ❋r❛❝t✐♦♥s ❘❡❝✐♣r♦❝❛❧s ❚✇♦ ♥✉♠❜❡rs ✇❤♦s❡ ♣r♦❞✉❝t ✐s ✶ ❛r❡ r❡❝✐♣r♦❝❛❧s ♦❢ ❡❛❝❤ ♦t❤❡r✳ ❋♦r ❡①❛♠♣❧❡✱ s✐♥❝❡ r❡❝✐♣r♦❝❛❧s ♦❢ ❡❛❝❤ ♦t❤❡r✳ ❙♦♠❡ ♦t❤❡r ♣❛✐rs ♦❢ r❡❝✐♣r♦❝❛❧s ❛r❡ ❧✐st❡❞ ❜❡❧♦✇✳ 4 5 · 5 4 = 1, 54 ❛♥❞ 5 4 ❛r❡ ✷✹ ❈❍❆P❚❊❘ ✶✳ 2 7 7, 2 3 4 4, 3 ❆❘■❚❍▼❊❚■❈ ❘❊❱■❊❲ 6 1 1, 6 ❘❡❝✐♣r♦❝❛❧s ❛r❡ ✉s❡❞ ✐♥ ❞✐✈✐s✐♦♥ ♦❢ ❢r❛❝t✐♦♥s✳ ❉✐✈✐s✐♦♥ ♦❢ ❋r❛❝t✐♦♥s ❚♦ ❞✐✈✐❞❡ ❛ ✜rst ❢r❛❝t✐♦♥ ❜② ❛ s❡❝♦♥❞ ❢r❛❝t✐♦♥✱ ♠✉❧t✐♣❧② t❤❡ ✜rst ❢r❛❝t✐♦♥ ❜② t❤❡ r❡❝✐♣r♦❝❛❧ ♦❢ t❤❡ s❡❝♦♥❞ ❢r❛❝t✐♦♥✳ ❘❡❞✉❝❡ ✐❢ ♣♦ss✐❜❧❡✳ ❚❤✐s ♠❡t❤♦❞ ✐s s♦♠❡t✐♠❡s ❝❛❧❧❡❞ t❤❡ ✏✐♥✈❡rt ❛♥❞ ♠✉❧t✐♣❧②✑ ♠❡t❤♦❞✳ ✶✳✻✳✺ ❙❛♠♣❧❡ ❙❡t ❇ P❡r❢♦r♠ t❤❡ ❢♦❧❧♦✇✐♥❣ ❞✐✈✐s✐♦♥s✳ ❊①❛♠♣❧❡ ✶✳✷✼ 1 3 1 3 ÷ 34 .

R❝✐s❡ ✶✳✶✶✷ 3 2 = 5 3 = 18 ? ❊①❡r❝✐s❡ ✶✳✶✶✸ 80 ? ✶✳✻ ❖♣❡r❛t✐♦♥s ✇✐t❤ ❋r❛❝t✐♦♥s ✻ ✶✳✻✳✶ ❖✈❡r✈✐❡✇ • • • ▼✉❧t✐♣❧✐❝❛t✐♦♥ ♦❢ ❋r❛❝t✐♦♥s ❉✐✈✐s✐♦♥ ♦❢ ❋r❛❝t✐♦♥s ❆❞❞✐t✐♦♥ ❛♥❞ ❙✉❜tr❛❝t✐♦♥ ♦❢ ❋r❛❝t✐♦♥s ✻ ❚❤✐s ❝♦♥t❡♥t ✐s ❛✈❛✐❧❛❜❧❡ ♦♥❧✐♥❡ ❛t ❁❤tt♣✿✴✴❝♥①✳♦r❣✴❝♦♥t❡♥t✴♠✷✶✽✻✼✴✶✳✷✴❃✳ ✭❙♦❧✉t✐♦♥ ♦♥ ♣✳ ✹✹✳✮ ✷✸ ✶✳✻✳✷ ▼✉❧t✐♣❧✐❝❛t✐♦♥ ♦❢ ❋r❛❝t✐♦♥s ▼✉❧t✐♣❧✐❝❛t✐♦♥ ♦❢ ❋r❛❝t✐♦♥s ❚♦ ♠✉❧t✐♣❧② t✇♦ ❢r❛❝t✐♦♥s✱ ♠✉❧t✐♣❧② t❤❡ ♥✉♠❡r❛t♦rs t♦❣❡t❤❡r ❛♥❞ ♠✉❧t✐♣❧② t❤❡ ❞❡♥♦♠✐♥❛t♦rs t♦❣❡t❤❡r✳ ❘❡❞✉❝❡ t♦ ❧♦✇❡st t❡r♠s ✐❢ ♣♦ss✐❜❧❡✳ ❊①❛♠♣❧❡ ✶✳✷✹ ❋♦r ❡①❛♠♣❧❡✱ ♠✉❧t✐♣❧② 3 4 3 4 1 6.

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