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math.AC2025
Ulrich modules over local rings of dimension two
Srikanth B. Iyengar, Linquan Ma, Mark E. Walker
It is proved that Ulrich modules exist for a large class of local rings of dimension two. This complements earlier work of the authors and Ziquan Zhuang that described complete int…
math.AC2025
Non-existence of Ulrich modules over Cohen-Macaulay local rings
Srikanth B. Iyengar, Linquan Ma, Mark E. Walker +1
Over a Cohen-Macaulay local ring, the minimal number of generators of a maximal Cohen-Macaulay module is bounded above by its multiplicity. In 1984 Ulrich asked whether there alway…