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Throughout abstract algebra, the term "magma" is most often used as a synonym of the more antiquated term "groupoid," referring to a set equipped with a binary operator. The ...

Let A be a commutative complex Banach algebra. The space of all characters on A is called the maximal ideal space (or character space) of A. This space equipped with the ...

Module multiplicity is a number associated with every nonzero finitely generated graded module M over a graded ring R for which the Hilbert series is defined. If dim(M)=d, ...

A monoid is a set that is closed under an associative binary operation and has an identity element I in S such that for all a in S, Ia=aI=a. Note that unlike a group, its ...

Let A be a non-unital C^*-algebra. There is a unique (up to isomorphism) unital C^*-algebra which contains A as an essential ideal and is maximal in the sense that any other ...

Let H be a complex Hilbert space, and define a nest as a set N of closed subspaces of H satisfying the conditions: 1. 0,H in N, 2. If N_1,N_2 in N, then either N_1 subset= ...

A number which is simultaneously octagonal and heptagonal. Let O_m denote the mth octagonal number and H_n the nth heptagonal number, then a number which is both octagonal ...

Attractive compounds of four octahedra can be constructed as the duals of the cube 4-compounds. These compounds will be implemented in a future version of the Wolfram ...

The ordinary Onsager equation is the sixth-order ordinary differential equation (d^3)/(dx^3)[e^x(d^2)/(dx^2)(e^x(dy)/(dx))]=f(x) (Vicelli 1983; Zwillinger 1997, p. 128), ...

PEMDAS is an acronym used primarily in the United States as a mechanism to pedagogically enforce the order rules of computational precedence. PEMDAS is explained as follows: ...