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The following equivalent definitions of a left perfect ring R are found in Anderson and Fuller: [2]. Every left R-module has a projective cover.; R/J(R) is semisimple and J(R) is left T-nilpotent (that is, for every infinite sequence of elements of J(R) there is an n such that the product of first n terms are zero), where J(R) is the Jacobson radical of R.
Let C be an additive category, or more generally an additive R-linear category for a commutative ring R. We call C a Krull–Schmidt category provided that every object decomposes into a finite direct sum of objects having local endomorphism rings. Equivalently, C has split idempotents and the endomorphism ring of every object is semiperfect.
In mathematics, a semiperfect magic cube is a magic cube that is not a perfect magic cube, i.e., a magic cube for which the cross section diagonals do not necessarily sum up to the cube's magic constant.
In mathematics, a semiprime is a natural number that is the product of exactly two prime numbers.The two primes in the product may equal each other, so the semiprimes include the squares of prime numbers.
Bridges was born on December 4, 1949, in Los Angeles, the son of actor Lloyd Bridges (1913–1998) [2] and actress and writer Dorothy Bridges (née Simpson; 1915–2009). He is one of four children: older brother Beau Bridges (born December 9, 1941), who is also an actor; a younger sister Lucinda; and a brother named Garrett, who died of sudden infant death syndrome in 1948.
In number theory, a Sierpiński number is an odd natural number k such that + is composite for all natural numbers n.In 1960, Wacław Sierpiński proved that there are infinitely many odd integers k which have this property.
In number theory, a k-hyperperfect number is a natural number n for which the equality = + (()) holds, where σ(n) is the divisor function (i.e., the sum of all positive divisors of n).
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