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Joseph A. Gallian (born January 5, 1942) is an American mathematician, the Morse Alumni Distinguished University Professor of Teaching in the Department of Mathematics and Statistics at the University of Minnesota Duluth.
Abstract algebra is the subject area of mathematics that studies algebraic structures, such as groups, rings, fields, modules, vector spaces, and algebras.The phrase abstract algebra was coined at the turn of the 20th century to distinguish this area from what was normally referred to as algebra, the study of the rules for manipulating formulae and algebraic expressions involving unknowns and ...
He is known for his lucid style of writing, as exemplified by his Topics in Algebra, an undergraduate introduction to abstract algebra that was first published in 1964, with a second edition in 1975. A more advanced text is his Noncommutative Rings [ 3 ] in the Carus Mathematical Monographs series.
In mathematics, more specifically algebra, abstract algebra or modern algebra is the study of algebraic structures, which are sets with specific operations acting on their elements. [1] Algebraic structures include groups , rings , fields , modules , vector spaces , lattices , and algebras over a field .
Contemporary Abstract Algebra (6e ed.). Houghton Mifflin. ISBN 0-618-51471-6. Linear algebra theory. Explains commutativity in chapter 1, uses it throughout. Goodman, Frederick (2003). Algebra: Abstract and Concrete, Stressing Symmetry (2e ed.). Prentice Hall. ISBN 0-13-067342-0. Abstract algebra theory. Uses commutativity property throughout book.
In abstract algebra, a normal subgroup (also known as an invariant subgroup or self-conjugate subgroup) [1] is a subgroup that is invariant under conjugation by members of the group of which it is a part.
In abstract algebra, group theory studies the algebraic structures known as groups. The concept of a group is central to abstract algebra: other well-known algebraic structures, such as rings, fields, and vector spaces, can all be seen as groups endowed with additional operations and axioms. Groups recur throughout mathematics, and the methods ...
Authors sometimes dub these proofs "abstract nonsense" as a light-hearted way of alerting readers to their abstract nature. Labeling an argument "abstract nonsense" is usually not intended to be derogatory, [2] [1] and is instead used jokingly, [3] in a self-deprecating way, [4] affectionately, [5] or even as a compliment to the generality of ...