
SalahEddine Kabbaj
King Fahd University of Petroleum and Minerals (KFUPM), Saudi Arabia

 Talk 1: The dimension of tensor products of pullbacks issued from AFdomains
Monday 8 March, 11:0012:00
Abstract:
We provide formulas for the Krull dimension (and valuative
dimension) of tensor products of kalgebras arising from pullbacks. Our
purpose is to compute dimensions of tensor products of two kalgebras for
a large class of (not necessarily AFdomain) kalgebras, moving therefore
beyond Sharp's and Wadsworth's contexts.
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 Talk 2: On the prime ideal structure of tensor products of kalgebras (Part I)
Tuesday 9 March, 11:0012:00
Abstract:
We aim at shedding light on spectra of tensor products of
kalgebras. Precisely, we'll study conditions under which tensor products
inherit crucial spectral properties (such as catenarity and strong
Sproperty). A close look to the minimal prime structure is then in
order. The results lead to new families of stably strong Srings 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 kalgebras (Part II)
Wednesday 10 March, 11:0012:00
Abstract:
Same as above
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 Talk 4: Two conjectures in dimension theory
Thursday 11 March, 11:0012:00
Abstract:
A finitedimensional domain R is said to be Jaffard if its
Krull and valuative dimensions coincide. The class of Jaffard domains
contains most of the wellknown classes of finitedimensional commutative
rings involved in dimension theory (such as Noetherian domains, Prufer
domains, universally catenarian domains, and stably strong Sdomains).
However, the question of establishing or denying a possible connection to
the family of Krulllike domains (e.g. UFDs and PVMDs) is still unsolved.
In this vein, Bouvier's conjecture (initially, announced in1985) sustains
that "finitedimensional 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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