AlgebraThere is no one best way for an undergraduate student to learn elementary algebra. Some kinds of presentations will please some learners and will disenchant others. This text presents elementary algebra organized accord ing to some principles of universal algebra. Many students find such a presentation of algebra appealing and easier to comprehend. The approach emphasizes the similarities and common concepts of the many algebraic structures. Such an approach to learning algebra must necessarily have its formal aspects, but we have tried in this presentation not to make abstraction a goal in itself. We have made great efforts to render the algebraic concepts intuitive and understandable. We have not hesitated to deviate from the form of the text when we feel it advisable for the learner. Often the presenta tions are concrete and may be regarded by some as out of fashion. How to present a particular topic is a subjective one dictated by the author's estima tion of what the student can best handle at this level. We do strive for consistent unifying terminology and notation. This means abandoning terms peculiar to one branch of algebra when there is available a more general term applicable to all of algebra. We hope that this text is readable by the student as well as the instructor. It is a goal of ours to free the instructor for more creative endeavors than reading the text to the students. |
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Common terms and phrases
a₁ a₂ algebraic alternatives completes annihilating ideal automorphism basis matrices bijection binary operation Cartesian product change of basis closure class coefficients commutative group commutative unitary ring completes a true congruence coset Definition denote direct sum endomorphism epimorphism equivalence relation example exists field finite basis finite number function given group G implies infinite integral domain invariant factor inverse isomorphic K-vector kernel ƒ Let G linear combination linearly independent linearly independent family M₁ M₂ matrix with entries module monoid monomorphism multiplication natural numbers neutral element nonzero normal subgroup notation nullary operation number of elements operational system permutation polynomial prime principal domain principal ideal domain PROOF Prove quotient set R-module r₁ r₂ range ƒ rank Show solution statements are true submodule subring subset subspace surjection theorem true sentence u₁ unitary monoid vector space X₁ Y₁ zero
References to this book
Annales Academiae Scientiarum Fennicae. Series A. I, Mathematica, Volume 13 No preview available - 1988 |