Universal algebra (sometimes called general algebra) is
the field of mathematics that studies algebraic structures themselves,
not examples ("models") of algebraic structures.
For instance, rather than take particular groups as the object of study,
in universal algebra one takes the class of groups as an object of study.
Zinbiel algebra or dual Leibniz algebra is a module over a commutative ring with
a bilinear product satisfying the defining identity:
Heyting algebra
Heyting algebra (also known as pseudo-Boolean algebra[1]) is a bounded lattice
(with join and meet operations written ∨ and ∧ and
with least element 0 and greatest element 1)
equipped with a binary operation a → b of implication such that
(c ∧ a) ≤ b is equivalent to c ≤ (a → b).
Associative algebra is an algebraic structure with
compatible operations of addition, multiplication (assumed to be associative),
and a scalar multiplication by elements in some field.
The addition and multiplication operations together give A the structure of a ring;
the addition and scalar multiplication operations together give A
the structure of a vector space over K.
K-algebra to mean an associative algebra over the field K.
A standard first example of a K-algebra is a ring of square matrices over a field K,
with the usual matrix multiplication.
Banach algebra, is an associative algebra A over the real or complex numbers
(or over a non-Archimedean complete normed field)
that at the same time is also a Banach space,
that is, a normed space that is complete in the metric induced by the norm.
The norm is required to satisfy
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