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A lattice L is said to be oriented if there exists a rule which assigns a specified direction to any edge connecting arbitrary lattice points x_i,x_j in L. In that way, an ...

Two lines, vectors, planes, etc., are said to be perpendicular if they meet at a right angle. In R^n, two vectors a and b are perpendicular if their dot product a·b=0. (1) In ...

A principal ideal domain is an integral domain in which every proper ideal can be generated by a single element. The term "principal ideal domain" is often abbreviated P.I.D. ...

Any ideal of a ring which is strictly smaller than the whole ring. For example, 2Z is a proper ideal of the ring of integers Z, since 1 not in 2Z. The ideal <X> of the ...

A typical vector (i.e., a vector such as the radius vector r) is transformed to its negative under inversion of its coordinate axes. Such "proper" vectors are known as polar ...

A figurate number corresponding to a configuration of points which form a pyramid with r-sided regular polygon bases can be thought of as a generalized pyramidal number, and ...

RSA numbers are difficult to-factor composite numbers having exactly two prime factors (i.e., so-called semiprimes) that were listed in the Factoring Challenge of RSA ...

By analogy with the squircle, a term first apparently used by Fernández Guasti et al. (2005), the term "rectellipse" (used here for the first time) is a natural ...

The term rectification is sometimes used to refer to the determination of the length of a curve. Rectification also refers to the operation which converts the midpoints of ...

Given a commutative unit ring R and a filtration F:... subset= I_2 subset= I_1 subset= I_0=R (1) of ideals of R, the Rees ring of R with respect to F is R_+(F)=I_0 direct sum ...