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If A is a graded module and there exists a degree-preserving linear map phi:A tensor A->A, then (A,phi) is called a graded algebra. Cohomology is a graded algebra. In ...

A popular acronym for "principal ideal domain." In engineering circles, the acronym PID refers to the "proportional-integral-derivative method" algorithm for controlling ...

A ringoid is a set R with two binary operators, conventionally denoted addition (+) and multiplication (×), where × distributes over + left and right: a(b+c)=ab+ac and ...

A semiring is a set together with two binary operators S(+,*) satisfying the following conditions: 1. Additive associativity: For all a,b,c in S, (a+b)+c=a+(b+c), 2. Additive ...

The zero product property asserts that, for elements a and b, ab=0=>a=0 or b=0. This property is especially relevant when considering algebraic structures because, e.g., ...

Let there be two particularly well-behaved functions F(x) and p_tau(x). If the limit lim_(tau->0)int_(-infty)^inftyp_tau(x)F(x)dx exists, then p_tau(x) is a regular sequence ...

A finite division algebra is a field.

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, ...

An almost unit is a nonunit in the integral domain of formal power series with a nonzero first coefficient, P=a_1x+a_2x^2+..., where a_1!=0. Under the operation of ...

The cokernel of a group homomorphism f:A-->B of Abelian groups (modules, or abstract vector spaces) is the quotient group (quotient module or quotient space, respectively) ...