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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. ...

A proper ideal I of a ring R is called semiprime if, whenever J^n subset I for an ideal J of R and some positive integer, then J subset I. In other words, the quotient ring ...

A connected graph having e graph edges is said to be sequential if it is possible to label the nodes i with distinct integers f_i in {0,1,2,...,e-1} such that when graph edge ...

The conjecture that all integers >1 occur as a value of the totient valence function (i.e., all integers >1 occur as multiplicities). The conjecture was proved by Ford ...

A T_1-space is a topological space fulfilling the T1-separation axiom: For any two points x,y in X there exists two open sets U and V such that x in U and y not in U, and y ...

A unique factorization domain, called UFD for short, is any integral domain in which every nonzero noninvertible element has a unique factorization, i.e., an essentially ...

An Argand diagram is a plot of complex numbers as points z=x+iy in the complex plane using the x-axis as the real axis and y-axis as the imaginary axis. In the plot above, ...

The pentanacci numbers are a generalization of the Fibonacci numbers defined by P_0=0, P_1=1, P_2=1, P_3=2, P_4=4, and the recurrence relation ...

The set of numbers generated by excluding the sums of two or more consecutive earlier members is called the prime numbers of measurement, or sometimes the segmented numbers. ...

A pair of numbers m and n such that sigma(m)=sigma(n)=m+n-1, where sigma(m) is the divisor function. Beck and Najar (1977) found 11 augmented amicable pairs.