Henry Cohn`s home page
... These notes are from a series of lectures given by Henry Cohn during MIT’s Independent Activities Period in January, 1995. They were first revised by Henry Cohn and Jon Hanke at PROMYS 1995 and then Joshua Greene worked on further revision at PROMYS 1996. The main references are A Classical Introduc ...
... These notes are from a series of lectures given by Henry Cohn during MIT’s Independent Activities Period in January, 1995. They were first revised by Henry Cohn and Jon Hanke at PROMYS 1995 and then Joshua Greene worked on further revision at PROMYS 1996. The main references are A Classical Introduc ...
notes
... of Br(k(X)), the Brauer group of the function field of X. A Brauer class α in Br(k(X)) is a form of a matrix algebra over k(X). Choose a representative A for the Brauer class α; thus A is a central simple algebra over k(X) such that [A] = α. In particular it is a finite dimensional vector space over ...
... of Br(k(X)), the Brauer group of the function field of X. A Brauer class α in Br(k(X)) is a form of a matrix algebra over k(X). Choose a representative A for the Brauer class α; thus A is a central simple algebra over k(X) such that [A] = α. In particular it is a finite dimensional vector space over ...
1 Localization
... Theorem 1.2. Let S be a multiplicative subset of A. Then there is an ideal P that is maximal with respect to inclusion among all the ideals contained in A \ S (i.e., P ∩ S = ∅). Furthermore, P is a prime ideal. Proof. This is another use of Zorn’s Lemma. Let M = {I ≤ A | I ∩ S = ∅}. Then M is an (pa ...
... Theorem 1.2. Let S be a multiplicative subset of A. Then there is an ideal P that is maximal with respect to inclusion among all the ideals contained in A \ S (i.e., P ∩ S = ∅). Furthermore, P is a prime ideal. Proof. This is another use of Zorn’s Lemma. Let M = {I ≤ A | I ∩ S = ∅}. Then M is an (pa ...
Real Composition Algebras by Steven Clanton
... If it satisfies only one of the identities it is called left or right distributive, respectively. ...
... If it satisfies only one of the identities it is called left or right distributive, respectively. ...
Commutative ring
... 19th century) realized that, unlike in Z, in many rings there is no unique factorization into prime numbers. (Rings where it does hold are called unique factorization domains.) By definition, a prime ideal is a proper ideal such that, whenever the product ab of any two ring elements a and b is in p, ...
... 19th century) realized that, unlike in Z, in many rings there is no unique factorization into prime numbers. (Rings where it does hold are called unique factorization domains.) By definition, a prime ideal is a proper ideal such that, whenever the product ab of any two ring elements a and b is in p, ...
Rings with no Maximal Ideals
... could take R = F [[x]], the ring of power series in x over F , or R = F [x](x) , the localization of the polynomial ring F [x] at the maximal ideal (x). We show that M has no maximal ideals. We point out that since R is a local ring with maximal ideal M , the group of units of R is R \ M . Furthermo ...
... could take R = F [[x]], the ring of power series in x over F , or R = F [x](x) , the localization of the polynomial ring F [x] at the maximal ideal (x). We show that M has no maximal ideals. We point out that since R is a local ring with maximal ideal M , the group of units of R is R \ M . Furthermo ...
