In abstract algebra, an associated prime of a moduleM over a ringR is a type of prime ideal of R that arises as an annihilator of a (prime) submodule of M. The set of associated primes is usually denoted by .
In commutative algebra, associated primes are linked to the Lasker-Noether primary decomposition of ideals in commutative Noetherian rings. Specifically, if an ideal J is decomposed as a finite intersection of primary ideals, the radicals of these primary ideals are prime ideals, and this set of prime ideals coincides with . Also linked with the concept of "associated primes" of the ideal are the notions of isolated primes and embedded primes.
Definitions
A nonzero R module N is called a prime module if the annihilator for any nonzero submodule N' of N. For a prime module N, is a prime ideal in R.
An associated prime of an R module M is an ideal of the form where N is a prime submodule of M. In commutative algebra the usual definition is different, but equivalent: if R is commutative, an associated prime P of M is a prime ideal of the form for a nonzero element m of M or equivalently is isomorphic to a submodule of M.
By The Associated Press. The New England Patriots have signed free agent wide receiver Stefon Diggs, a person familiar with the deal told The Associated Press, giving quarterback Drake Maye a prime target as he heads into his second season.
(AP) — The New England Patriots have signed free agent wide receiver Stefon Diggs, a person familiar with the deal told The Associated Press, giving quarterback Drake Maye a prime target as he heads into his second season.
In a communication addressed to PrimeMinister Olzhas Bektenov, Peruaşev said, “A crypto bank, an institution that will take over the functions of the oversight, exchange, and storage of digital ...
His predecessor Boris Yeltsin had stepped down on 31 December1999, appointing his young prime minister in his place to prevent political opponents from prosecuting him and his associates – on well-founded grounds – for corruption ... REGISTER ... ×. .
FOXBOROUGH, Mass. (AP) — The New England Patriots have signed free agent wide receiver Stefon Diggs, a person familiar with the deal told The Associated Press, giving quarterback Drake Maye a prime target as he heads into his second season ... .
The bank cited the decreases in yuan loan prime rates and interest rates associated with the outstanding mortgages amid Beijing's push to reinvigorate the property market as reasons for the decline ...The StandardChannel. IOSAndroid. IOS Android ... .
Ronen Bar will leave his position in two weeks (on April 10) or whenever the prime minister appoints his replacement, whichever comes first ... What complicates matters is the fact that the third man is associated with the political left.
In 2008, when he went to inspect the plot, he noticed that a company called PrimeProperty Developers was constructing buildings there. “When I asked for the documents, Gupta and his associates ...
"Pakistan has to increase the share of agriculture in the country's economy as about 65 percent of our population, directly or indirectly, is associated with agriculture," the prime minister said during an event here on Monday.