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  2. Abstrakt Algebra - Wikipedia

    en.wikipedia.org/wiki/Abstrakt_Algebra

    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.

  3. Band (algebra) - Wikipedia

    en.wikipedia.org/wiki/Band_(algebra)

    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]

  4. Abstract algebra - Wikipedia

    en.wikipedia.org/wiki/Abstract_algebra

    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 .

  5. Medial magma - Wikipedia

    en.wikipedia.org/wiki/Medial_magma

    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 ...

  6. Free monoid - Wikipedia

    en.wikipedia.org/wiki/Free_monoid

    In abstract algebra, the free monoid on a set is the monoid whose elements are all the finite sequences (or strings) of zero or more elements from that set, with string concatenation as the monoid operation and with the unique sequence of zero elements, often called the empty string and denoted by ε or λ, as the identity element.

  7. Magma (algebra) - Wikipedia

    en.wikipedia.org/wiki/Magma_(algebra)

    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 ...

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