#### 2013 Japan international wind power exhibition

: Time: February 27 – March 1, 2013 Closing time: March 1, 2013 Exhibition venues: Tokyo Interna … more →

Tags: lighting, Silent Generator

#### CSR Corporation Limited will launch low wind speed wind generator

: China’s first 7 m / s wind speed low wind speed wind generating sets are applied to in CSR Zhu … more →

Tags: lighting, Silent Generator

#### China International power equipment and generators exhibition 2013

: Exhibition Dates: April 8 – 10, 2013 Exhibition Venue: Shanghai New International Expo Center … more →

Tags: lighting, Silent Generator

#### 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 … more →

#### Characterize the left ideal of a semigroup generated by a subset

: 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

: 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

: Let be a semigroup and let be a nonempty subset. Recall that the subsemigroup of generated by is the … more →

Tags: isp, semigroup, subsemigroup

#### 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

: 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

: 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

: In TAN, we defined the product of (finitely generated) ideals and to be . We can also define an idea … more →

Tags: TAN:PD, Ideal, ring, Product

#### (A) is contained in I if and only if A is contained in I

: Let be a commutative ring, let be an ideal, and let be a subset. Prove that if and only if . Certain … more →

Tags: TAN:PD, Ideal

#### Show that a given generating set is a basis for an ideal in a quadratic integer ring

: 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

: Let be a field and let be an extension of . Suppose is finitely generated as an -vector space; say b … more →

Tags: TAN:PD, degree, field extension

#### Two basic properties of ideal quotients

: 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

: 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

: 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

: 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

: Suppose is a subset and a finitely generated ideal. Then there exists a finite subset such that . Le … more →