Emmy Noether representa un punt d’inflexió fonamental en el desenvolupament de l’Àlgebra Commutativa. Per una banda, en ella conflueixen algunes de les línies evolutives prèvies més importants. Per altra, a partir del seu ...

Let $G_n$ be a double cover of either the alternating group $A_n$ or the symmetric group $S_n$, and let $G_{n-1}$ be the corresponding double cover of $A_{n-1}$ or $S_{n-1}$. For every odd $n\geq 3$ and every field $k$ of ...

This paper takes a new look at ideals generated by 2×2 minors of 2×3 matrices whose entries are powers of three elements not necessarily forming a regular sequence. A special case of this is the ideals determining monomial ...

Let R be a Noetherian local ring. We prove that R is regular of dimension at most 4 if, and only if, every prime ideal, defining a Gorenstein quotient ring, is syzygetic. We deduce a characterization of these rings in terms ...

Resolution of singularities in algebraic varieties has been a topic of interest in commutative algebra and algebraic geometry during the last decades. Altough we have a theory of resolution of singularities for rings of ...

Les F-singularitats són singularitats d'anells commutatius de característica primera relacionats amb l'endomorfisme de Frobenius. Per a poder-les estudiar, s'han introduit invariants numèrics com la multiplicitat de ...

Let $I$ be an ideal of a commutative Noetherian ring $A$, $A\supset \Q$, $B=A/I$ and ${\bf G}(I)$ the associated graded ring to $I$. It is known that $H_{2}(A,B,B)=0$ is equivalent to $I$ being syzygetic. We prove that the ...