Blogs about: Generating Set
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A generating set for the kernel of a given module homomorphism
Let , , , et cetera be as in this previous exercise. Show that is generated by . Let . Now , and by this previous exercise, we have . Recall that the are in , so that for some . Since the are a basis… more →
Project Crazy Project
2013 Japan international wind power exhibition
wrote 3 months ago: Time: February 27 – March 1, 2013 Closing time: March 1, 2013 Exhibition venues: Tokyo Interna … more →
CSR Corporation Limited will launch low wind speed wind generator
wrote 3 months ago: China’s first 7 m / s wind speed low wind speed wind generating sets are applied to in CSR Zhu … more →
China International power equipment and generators exhibition 2013
wrote 3 months ago: Exhibition Dates: April 8 – 10, 2013 Exhibition Venue: Shanghai New International Expo Center … more →
A generating set for the kernel of a given module homomorphism
wrote 1 year ago: Let , , , et cetera be as in this previous exercise. Show that is generated by . Let . Now , and by … more →
Characterize the left ideal of a semigroup generated by a subset
wrote 1 year ago: Let be a semigroup and let be a nonempty subset. Recall that the left ideal of generated by is the i … more →
Exhibit a semigroup which is not finitely generated and a semigroup which is finitely generated but not cyclic
wrote 1 year ago: Exhibit a semigroup which is not finitely generated and a semigroup which is finitely generated but … more →
Characterization of the subsemigroup generated by a subset
wrote 1 year ago: Let be a semigroup and let be a nonempty subset. Recall that the subsemigroup of generated by is the … more →
While every ideal in an algebraic integer ring is generated by two elements, an arbitrary generating set need not contain a two-element generating set
wrote 1 year ago: Exhibit an ideal such that but is not equal to any of , , and . Consider , and note that , , and . … more →
Given an element a of an ideal in an algebraic integer ring, give a two element generating set containing a
wrote 1 year ago: Find such that in . Find such that in . Note that . Using Theorem 9.3, it suffices to find an elemen … more →
An equivalent characterization of ideal products
wrote 1 year ago: In TAN, we defined the product of (finitely generated) ideals and to be . We can also define an idea … more →
(A) is contained in I if and only if A is contained in I
wrote 1 year ago: Let be a commutative ring, let be an ideal, and let be a subset. Prove that if and only if . Certain … more →
Show that a given generating set is a basis for an ideal in a quadratic integer ring
wrote 1 year ago: Show that is a basis for the ideal in . First we wish to show that ; the direction is clear. Now sup … more →
A fact about finitely generated field extensions
wrote 1 year ago: Let be a field and let be an extension of . Suppose is finitely generated as an -vector space; say b … more →
Two basic properties of ideal quotients
wrote 2 years ago: Recall that if is a ring with ideals and , the ideal quotient in is defined to be . This set is cert … more →
Every monomial ideal has a unique inclusion-minimal monomial generating set
wrote 2 years ago: Let be a field, and let be a monomial ideal. Suppose is an inclusion-minimal generating set for . Pr … more →
Every monomial generating set is a Gröbner basis
wrote 2 years ago: Let be a monomial ideal with monomial generating set . Use Buchberger’s Criterion to show that … more →
Every monomial generating set is a Gröbner basis
wrote 2 years ago: Let be a field. Suppose is a monomial ideal with monomial generating set . Prove that is a Gröbner b … more →
In a Noetherian ring, any given generating set is equivalent to some of its finite subsets
wrote 2 years ago: Suppose is a subset and a finitely generated ideal. Then there exists a finite subset such that . Le … more →
Find a generating set for the augmentation ideal of a group ring
wrote 2 years ago: Let be a commutative ring with and a finite group. Prove that the augmentation ideal in the group ri … more →
