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The algebra structure of linear functionals on polynomials of a single variable (Roman 1984, pp. 2-3).

An Auslander algebra which connects the representation theories of the symmetric group of permutations and the general linear group GL(n,C). Schur algebras are ...

Let A be an involutive algebra over the field C of complex numbers with involution xi|->xi^♯. Then A is a left Hilbert algebra if A has an inner product <·,·> satisfying: 1. ...

An algebra with no nontrivial nilpotent ideals. In the 1890s, Cartan, Frobenius, and Molien independently proved that any finite-dimensional semisimple algebra over the real ...

There are at least two distinct (though related) notions of the term Hilbert algebra in functional analysis. In some literature, a linear manifold A of a (not necessarily ...

The group algebra K[G], where K is a field and G a group with the operation *, is the set of all linear combinations of finitely many elements of G with coefficients in K, ...

Let X be a set of urelements that contains the set N of natural numbers, and let V(X) be a superstructure whose individuals are in X. Let V(^*X) be an enlargement of V(X), ...

A partial algebra is a pair A=(A,(f_i^A)_(i in I)), where for each i in I, there are an ordinal number alpha_i and a set X_i subset= A^(alpha_i) such that f_i^A is a function ...

A Banach algebra is an algebra B over a field F endowed with a norm ||·|| such that B is a Banach space under the norm ||·|| and ||xy||<=||x||||y||. F is frequently taken to ...

An algebra in which the associator (x,x,x)=0. The subalgebra generated by one element is associative.