[Turkmath:5668] Hacettepe Üniversitesi Bölüm Semineri-Olgür Çelikbaş

[Asli Pekcan]

Sayın Liste Üyeleri,

Hacettepe Üniversitesi Matematik Bölümü genel seminerlerimiz kapsamında, 15
Haziran 2022 tarihinde saat 14:00'te bölümümüz Yaşar Ataman toplantı
salonunda yüz yüze gerçekleştirilecek, West Virginia University'den *Olgür *
*Çelikbaş*'ın vereceği "*On a theorem of Huneke and Wiegand*" başlıklı
konuşmaya
hepinizi bekleriz. Konuşmanın özeti aşağıda yer almaktadır.

Saygılarımla,
Aslı Pekcan


*Konuşmacı:*  Olgür Çelikbaş
*Konuşma Özeti:* Tensor products are important and ubiquitous objects in
mathematics, and they are used in many application areas, including physics
and engineering. In 1961 Auslander initiated the study of torsion in tensor
products of modules. In particular Auslander proved that (Lichtenbaum
(1966) in the ramified case), if R is a regular local ring and the tensor
product of two nonzero finitely generated R-modules M and N is
torsion-free, then M and N are both torsion-free. In 1994 Huneke and
Wiegand proved a partial extension of the aforementioned result of
Auslander, and obtained the following which is known as the second rigidity
theorem: if R is a local hypersurface ring and the tensor product of two
nonzero finitely generated R-modules M and N is reflexive, where N has rank
(for example, N has finite projective dimension), then M is reflexive. The
theme of the talk is the following question which stems from Huneke and
Wiegand (2007): If R, M, and N are as in the second rigidity theorem, then
are M and N both reflexive? I will discuss an example  which gives a
negative answer to the question. If there is time, I also plan to mention
some works that yield affirmative answers to the question under certain
additional conditions.
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