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