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Abstrakt Algebra was a Swedish experimental metal band with influences from power metal and doom metal. It was founded by bassist Leif Edling in 1994, shortly after his main project Candlemass split up. They made one album, but Edling had already started working on a second album with a different line-up.
A free magma M X on a set X is the "most general possible" magma generated by X (i.e., there are no relations or axioms imposed on the generators; see free object). The binary operation on M X is formed by wrapping each of the two operands in parentheses and juxtaposing them in the same order. For example: a • b = (a)(b), a • (a • b) = (a ...
The free group F S with free generating set S can be constructed as follows. S is a set of symbols, and we suppose for every s in S there is a corresponding "inverse" symbol, s −1, in a set S −1. Let T = S ∪ S −1, and define a word in S to be any written product of elements of T. That is, a word in S is an element of the monoid ...
In abstract algebra, a medial magma or medial groupoid is a magma or groupoid (that is, a set with a binary operation) that satisfies the identity (x • y) • (u • v) = (x • u) • (y • v), or more simply, xy • uv = xu • yv. for all x, y, u and v, using the convention that juxtaposition denotes the same operation but has higher ...
A normal band is a band S satisfying zxyz = zyxz for all x, y, and z ∈ S. We can also say a normal band is a band S satisfying axyb = ayxb for all a, b, x, and y ∈ S. This is the same equation used to define medial magmas, so a normal band may also be called a medial band, and normal bands are examples of medial magmas. [3]
A congruence on an algebra is an equivalence relation that forms a subalgebra of considered as an algebra with componentwise operations. One can make the set of equivalence classes A / Φ {\displaystyle A/\Phi } into an algebra of the same type by defining the operations via representatives; this will be well-defined since Φ {\displaystyle ...
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In algebra, a branch of pure mathematics, an algebraic structure consists of one or more sets closed under one or more operations, satisfying some axioms. Abstract algebra is primarily the study of algebraic structures and their properties. The notion of algebraic structure has been formalized in universal algebra
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