Algebra Seminar at Georgia State University

Spring 2008, Wednesdays 3:30-4:30pm, Paul Erdos Conference room (796) COE

February 6, Sara Malec, Georgia State
Noetherian filtrations (II)

Abstract:
The talk will present the equivalence between essentially power filtrations of ideals and Noetherian filtrations over Noetherian rings.
January 30, Sara Malec, Georgia State
Noetherian filtrations

Abstract:
The talk will present the foundations of the theory of Noetherian filtration of ideals.
January 23, Yongwei Yao, Georgia State
An example of Hochster concerning Spec(Q[[x,y,z]]) (III)

Abstract:
We will present an example of Hochster that shows that the map SpecQ[[x,y,z]] to SpecQ[x,y,z] is not open.
January 15, Yongwei Yao, Georgia State
An example of Hochster concerning Spec(Q[[x,y,z]]) (II)

Abstract:
We will present an example of Hochster that shows that the map SpecQ[[x,y,z]] to SpecQ[x,y,z] is not open.

August 22, Florian Enescu, Georgia State
Noether Normalization (I)

Abstract:
We will present the Noether Normalization Theorem based on a treatment of Y. Akizuki.
August 29, Florian Enescu, Georgia State
Noether Normalization (II)

Abstract:
We will present the Noether Normalization Theorem based on a treatment of Y. Akizuki.
September 5, Sara Malec, Georgia State
Graded rings and modules and their associated primes

Abstract: The talk will present graded rings and modules and highlight the main results about their associated primes.
September 12, Sara Malec, Georgia State
Graded rings and modules and their associated primes (II)

Abstract: The talk will present graded rings and modules and highlight the main results about their associated primes.
September 19, Sara Malec, Georgia State
Graded rings and modules and their associated primes (III)

Abstract: The talk will present graded rings and modules and highlight the main results about their associated primes.
September 26, Muslim Baig, Georgia State
The Spectrum of a Ring

Abstract: We will discuss the spectrum of a ring, its importance to algebraic geometry and some properties of the associated Zariski topology.
October 3, Muslim Baig, Georgia State
The Spectrum of a Ring (II)

Abstract: We will discuss the spectrum of a ring, its importance to algebraic geometry and some properties of the associated Zariski topology.
October 10, Muslim Baig, Georgia State
The Spectrum of a Ring (III)

Abstract: We will discuss the compactness of the spectrum, the generic points, and maps between spectra.
October 17, Muslim Baig, Georgia State
The Spectrum of a Ring (IV)

Abstract: We will discuss the compactness of the spectrum, the generic points, and maps between spectra.
October 24, Florian Enescu, Georgia State
Elements of dimension theory

Abstract: We will present a quick review of Krull dimension with emphasis on computation.
October 31, Jong Wook Kim, Georgia State
Spec of Z[x].

Abstract: We will present a detailed computation of Spec(Z[x]).
November 7, Sara Malec, Georgia State
Rings of dimension zero

Abstract: We will present the main results about the theory of Noetherian rings of dimension zero.
November 14, Jong Wook Kim, Georgia State
The principal ideal theorem.

Abstract: We will present a proof of Krull's principal ideal theorem.
November 16 SPECIAL LOCATION 140 COE 2-3pm, Jinjia Li, Syracuse University
On nonrigidity of Frobenius

Abstract: In a commutative ring R of prime characteristic p, the Frobenius map is an endomorphism of R sending an element in R to its p-th power. It is a very powerful tool in the study of commutative algebras and homological properties of algebras. The homological properties of the Frobenius map had been studied for decades, starting with the work of Kunz which states that flatness of Frobenius detects the regularity of the ring. In this talk, I will discuss the rigidity issue of the Frobenius map. In particular, I will talk about several surprising examples of Gorenstein local rings with nonrigid Frobenius, which are quite different from the complete intersection case, where Frobenius is known to be rigid. These examples answer negatively a question raised by Avramov and Miller.
December 5, Yongwei Yao, Georgia State
An example of Hochster concerning Spec(Q[[x,y,z]]) (I)

Abstract:
We will present an example of Hochster that shows that the map SpecQ[[x,y,z]] to SpecQ[x,y,z] is not open.
The Georgia State University-University of South Carolina Commutative Algebra Seminar takes place twice every semester, the location alternating between Atlanta and Columbia. For the upcoming seminar, go to GSU-USC Commutative Algebra seminar .