Mathematics - Research News

$b$-vectors of chordal graphs

 Mathematics - Research News
 05 January 2021
Luis Pedro Montejano, Luis Núñez-Betancourt. Source: Journal of Commutative Algebra, Volume 12, Number 4, 539--557.Abstract: The [math] -vector [math] of a graph [math] is defined in terms of its clique vector [math] by the equation [math] where [math] is the largest cardinality of a clique in...

The sets of star and semistar operations on semilocal Prüfer domains

 Mathematics - Research News
 05 January 2021
Dario Spirito. Source: Journal of Commutative Algebra, Volume 12, Number 4, 581--602.Abstract: We study the sets of semistar and star operations on a semilocal Prüfer domain, with an emphasis on which properties of the domain are enough to determine them. In particular, we show that these sets...

Frobenius split subvarieties pull back in almost all characteristics

 Mathematics - Research News
 05 January 2021
David E Speyer. Source: Journal of Commutative Algebra, Volume 12, Number 4, 573--579.Abstract: Let [math] and [math] be schemes of finite type over [math] and let [math] be a finite map. We show the following holds for all sufficiently large primes [math] : If [math] and [math] are any splittings...

$F$-pure threshold and height of quasihomogeneous polynomials

 Mathematics - Research News
 05 January 2021
Susanne Müller. Source: Journal of Commutative Algebra, Volume 12, Number 4, 559--572.Abstract: The aim of this paper is to give a connection between the [math] -pure threshold of a polynomial and the height of the corresponding Artin–Mazur formal group. For this, we consider a quasihomogeneous...

$\star$-super potent domains

 Mathematics - Research News
 05 January 2021
Evan Houston, Muhammad Zafrullah. Source: Journal of Commutative Algebra, Volume 12, Number 4, 489--507.Abstract: For a finite-type star operation [math] on a domain [math] , we say that [math] is [math] -super potent if each maximal [math] -ideal of [math] contains a finitely generated ideal...

A converse to a construction of Eisenbud–Shamash

 Mathematics - Research News
 05 January 2021
Petter A. Bergh, David A. Jorgensen, W. Frank Moore. Source: Journal of Commutative Algebra, Volume 12, Number 4, 467--477.Abstract: Let [math] be a commutative local Noetherian ring, [math] a [math] -regular sequence in [math] , and [math] . Given a complex of finitely generated free [math]...

On the sum of $z$-ideals in subrings of $C(X)$

 Mathematics - Research News
 05 January 2021
Fariborz Azarpanah, Mehdi Parsinia. Source: Journal of Commutative Algebra, Volume 12, Number 4, 459--466.Abstract: Let [math] be a Tychonoff space and [math] be an intermediate subalgebra of [math] , i.e., [math] . We show that such subrings are precisely absolutely convex subalgebras of [math] ....

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