## Viewing Abstract Algebra topics

The following topics are immediate sub-topics of Abstract Algebra.

• #### Term: Abelian Group

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• Definition: An abelian group is a group whose law of composition is commutative.

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• Definition: Let T: V -> V be a linear operator on a Hermitian space V, and let A be the matrix of T with respect to an orthonormal basis B. The adjoint operator T*: V -> V is the operator whose matrix with re...
• #### Term: Algebraically Closed

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• Definition: A field F is algebraically closed if every polynomial of positive degree with coefficients in F has a root in F.
• #### Term: Algebraic Integer

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• Definition: An algebraic number is an algebraic integer if its (monic) irreducible polynomial over Q has integer coefficients.
• #### Term: Algebraic Number Field

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• Definition: A number field K is a subfield of C, the field of complex numbers. Any subfield of C contains the field Q of rational numbers, so it is a field extension of Q. The number fields most commonly stu...
• #### Term: Algebraic Variety

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• Definition: A subset V of complex n-space C^n that is the set of common zeros of a finite number of polynomials in n variables is called an algebraic variety, or just a variety.
• #### Term: Alternating Group

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• Definition: The kernel of the sign homomorphism is called the alternating group. It consists of the even permutations, and is denoted by A_n.
• #### Term: Ascending Chain Condition

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• Definition: The ascending chain condition, commonly abbreviated "A.C.C.," for a partially ordered set X requires that all increasing sequences in X become eventually constant. A module M fulfills the ascending...
• #### Term: Associates

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