A remark on the spectra of rings with Gabriel dimension
A remarkable contraction of semisimple Lie algebras
Recently, E.Feigin introduced a very interesting contraction of a semisimple Lie algebra (see arXiv:1007.0646 and arXiv:1101.1898). We prove that these non-reductive Lie algebras retain good invariant-theoretic properties of . For instance, the algebras of invariants of both adjoint and coadjoint representations of are free, and also the enveloping algebra of is a free module over its centre.
A short proof of Krull's intersection theorem
A simple solution of Hilbert's fourteenth problem in dimension five
We give a short proof of a counterexample (due to Daigle and Freudenburg) to Hilbert's fourteenth problem in dimension five.
A spectral construction of a treed domain that is not going-down
A strong complement property of Dedekind domains
A subspace of and its connexions with the maximal ring of quotients
A Survey of Counterexamples to Hilbert's Fourteenth Problem
We survey counterexamples to Hilbert’s Fourteenth Problem, beginning with those of Nagata in the late 1950s, and including recent counterexamples in low dimension constructed with locally nilpotent derivations. Historical framework and pertinent references are provided. We also include 8 important open questions.
A theorem on normal flatness
A theory of multiplicity for multiplictive filtrations.
A two-dimensional domain whose integral closure is not t-linked.
A uniform Artin-Rees theorem and Zariski's main lemma on holomorphic functions.
A “-operation free” approach to Prüfer -multiplication domains.
Abhyankar places admit local uniformization in any characteristic
Absolutely S-domains and pseudo-polynomial rings
A domain R is called an absolutely S-domain (for short, AS-domain) if each domain T such that R ⊆ T ⊆ qf(R) is an S-domain. We show that R is an AS-domain if and only if for each valuation overring V of R and each height one prime ideal q of V, the extension R/(q ∩ R) ⊆ V/q is algebraic. A Noetherian domain R is an AS-domain if and only if dim (R) ≤ 1. In Section 2, we study a class of R-subalgebras of R[X] which share many spectral properties with the polynomial ring R[X] and which we call pseudo-polynomial...
Actions of finite groups on C*-algebras.
Actions of Hopf algebras on pro-semisimple noetherian algebras and their invariants
Let H be a Hopf algebra over a field k such that every finite-dimensional (left) H-module is semisimple. We give a counterpart of the first fundamental theorem of the classical invariant theory for locally finite, finitely generated (commutative) H-module algebras, and for local, complete H-module algebras. Also, we prove that if H acts on the k-algebra A = k[[X₁,...,Xₙ]] in such a way that the unique maximal ideal in A is invariant, then the algebra of invariants is a noetherian Cohen-Macaulay...
Adem relations in the Dyer-Lashof algebra and modular invariants.
AK-invariant, some conjectures, examples and counterexamples
In my talk I am going to remind you what is the AK-invariant and give examples of its usefulness. I shall also discuss basic conjectures about this invariant and some positive and negative results related to these conjectures.
Alcune proprietà delle varietà algebriche reali