“Bulletin Board”

 School of Mathematics - February 28, 2004

Mathematical Lectures

Salah-Eddine Kabbaj
King Fahd University of Petroleum and Minerals (KFUPM),
Saudi Arabia

March 3-12, 2004
School of Mathematics, IPM

 
 

Salah-Eddine Kabbaj
King Fahd University of Petroleum and Minerals (KFUPM),
Saudi Arabia


  • Talk 1: The dimension of tensor products of pullbacks issued from AF-domains
    Monday 8 March, 11:00-12:00

    Abstract:
    We provide formulas for the Krull dimension (and valuative dimension) of tensor products of k-algebras arising from pullbacks. Our purpose is to compute dimensions of tensor products of two k-algebras for a large class of (not necessarily AF-domain) k-algebras, moving therefore beyond Sharp's and Wadsworth's contexts.

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  • Talk 2: On the prime ideal structure of tensor products of k-algebras (Part I)
    Tuesday 9 March, 11:00-12:00

    Abstract:
    We aim at shedding light on spectra of tensor products of k-algebras. Precisely, we'll study conditions under which tensor products inherit crucial spectral properties (such as catenarity and strong S-property). A close look to the minimal prime structure is then in order. The results lead to new families of stably strong S-rings and universally catenarian rings. Some examples illustrate the limits of these results.

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  • Talk 3: On the prime ideal structure of tensor products of k-algebras (Part II)
    Wednesday 10 March, 11:00-12:00

    Abstract:
    Same as above

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  • Talk 4: Two conjectures in dimension theory
    Thursday 11 March, 11:00-12:00

    Abstract:
    A finite-dimensional domain R is said to be Jaffard if its Krull and valuative dimensions coincide. The class of Jaffard domains contains most of the well-known classes of finite-dimensional commutative rings involved in dimension theory (such as Noetherian domains, Prufer domains, universally catenarian domains, and stably strong S-domains). However, the question of establishing or denying a possible connection to the family of Krull-like domains (e.g. UFDs and PVMDs) is still unsolved. In this vein, Bouvier's conjecture (initially, announced in1985) sustains that "finite-dimensional Krull domains, or more particularly UFDs, need not be Jaffard domains". As the Krull property is stable under adjunction of indeterminates, the problem merely deflates to the existence of a Krull domain R such that dim(R[X]) does not collapse to dim(R)+1. This is still outstanding.

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Information:
Place: School of Mathematics, Niavaran Bldg., Niavaran Square, Tehran, Iran.

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