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Titlebook: Algebra; Serge Lang Textbook 2002Latest edition Springer Science+Business Media New York 2002 Algebra Textbook.Category theory.Textbook.al

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Groupsalso called their . under the law of composition, and will be denoted by .. (Sometimes, we also write . · ., and in many cases it is also convenient to use an additive notation, and thus to write . + .. In that case, we call this element the . of . and .. It is customary to use the notation . + . only when the relation . + . = . + . holds.)
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Algebraic Extensionshere the polynomial has a root, and we prove the existence of an algebraic closure. We make a preliminary study of such extensions, including the automorphisms, and we give algebraic extensions of finite fields as examples.
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Structure of Bilinear Forms theorems giving normalized expressions for these forms with respect to suitable bases. The chapter also follows the standard pattern of decomposing an object into a direct sum of simple objects, insofar as possible.
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