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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.
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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.
This is a list of government-owned companies of Ethiopia. A Government-owned corporation is a legal entity that undertakes commercial activities on behalf of an owner government . There is no standard definition of a government-owned corporation (GOC) or state-owned enterprise (SOE), although the two terms can be used interchangeably.
In 2009 Ethiopia was a source country for men, women, and children subjected to trafficking in persons, specifically conditions of forced labor and forced prostitution. Girls from Ethiopia's rural areas were forced into domestic servitude and, less frequently, commercial sexual exploitation , while boys were subjected to forced labor in ...
A ring R is left self-injective if the module R R is an injective module. While rings with unity are always projective as modules, they are not always injective as modules. semiperfect A semiperfect ring is a ring R such that, for the Jacobson radical J(R) of R, (1) R/J(R) is semisimple and (2) idempotents lift modulo J(R). semiprimary
A semiperfect number is a natural number that is equal to the sum of all or some of its proper divisors. A semiperfect number that is equal to the sum of all its proper divisors is a perfect number. Most abundant numbers are also semiperfect; abundant numbers which are not semiperfect are called weird numbers.
Many of Price's works, including this, were lost for a long time and were found again in 2009. Ethiopia's Shadow was performed by the University of Arkansas Symphony Orchestra in January 2015. [ 3 ] On September 30, 2018, Jordan Randall Smith conducted the Hopkins Concert Orchestra in a performance he claims is the first East Coast performance.