Related papers: Monomial structures, I

We study notions such as finite presentability and coherence, for partially ordered abelian groups and vector spaces. Typical results are the following: (i) A partially ordered abelian group G is finitely presented if and only…

Given a morphism $f: X \rightarrow S$ of complex algebraic varieties and a constructible sheaf $\mathcal{G}$ on $X$, we compute the local monodromy of $Rf_*(\mathcal{G})$ and $Rf_!(\mathcal{G})$ in terms of the local monodromy of…

If G is a non-cyclic finite group, non-isomorphic G-sets X, Y may give rise to isomorphic permutation representations C[X] and C[Y]. Equivalently, the map from the Burnside ring to the representation ring of G has a kernel. Its elements are…

Given a collection $\{ G_i\}_{i=1}^d$ of finite groups and a ring $R$, we define a subring of the ring $M_n(R)$ ($n = \sum_{i=1}^d|G_i|)$ that encompasses all the individual group rings $R[G_i]$ along the diagonal blocks as $G_i$-circulant…

In the previous article 'A Mackey-functor theoretic interpretation of biset functors', we have constructed the 2-category $\mathbb{S}$ of finite sets with variable finite group actions, in which bicoproducts and bipullbacks exist. As shown…

Let G be a finite group. To every smooth G-action on a compact, connected and oriented surface we can associate its data of singular orbits. The set of such data becomes an Abelian group B_G under the G-equivariant connected sum. We will…

We study relationships between certain algebraic properties of groups and rings definable in a first order structure or $*$-closed in a compact $G$-space. As a consequence, we obtain a few structural results about $\omega$-categorical rings…

The class of finitely presented algebras A over a field K with a set of generators x_{1},...,x_{n} and defined by homogeneous relations of the form x_{i_1}x_{i_2}...x_{i_l}=x_{sigma(i_1)}x_{sigma(i_2)}...x_{sigma(i_l)}, where l geq 2 is a…

In this article, we describe the lattice of ideals of some Green biset functors. We consider Green biset functors which satisfy that each evaluation is a finite dimensional split semisimple commutative algebra and use the idempotents in…

In previous work we introduced the notion of binomial cup-one algebras, which are differential graded algebras endowed with Steenrod $\cup_1$-products and compatible binomial operations. In this paper we show that binomial cup-one algebras…

Using the group $G(1)$ of invertible elements and the maximal ideals $\mathfrak{m}_x$ of the commutative algebra $C(X)$ of real-valued functions on a compact regular space $X$, we define a Borel action of the algebra on the measure space…

As mathematical induction is applied to prove statements on natural numbers, {\it continuous induction} (or, {\it real induction}) is a tool to prove some statements in real analysis.(Although, this comparison is somehow an overstatement.)…

Let G be a finite group that acts on an abelian monoid A. If f: A -> G is a map so that f(a f(a)(b)) = f(a)f(b), for all a, b in A, then the submonoid S = {(a, f(a)) | a in A} of the associated semidirect product of A and G is said to be a…

Let $G$ be an $\ell$-group (which is short for ``lattice-ordered abelian group''). Baker and Beynon proved that $G$ is finitely presented iff it is finitely generated and projective. In the category $\mathcal U$ of {\it unital}…

Given a torsion theory (Y,X) in an abelian category C, the reflector I from C to the torsion-free subcategory X induces a reflective factorisation system (E, M) on C. It was shown by A. Carboni, G.M. Kelly, G. Janelidze and R. Par\'e that…

We introduce two spaces $\Omega(\Gamma,G)$ and $\Omega(P_{\Gamma,G})$ of pre-partition functions and of opposite series, respectively, which are associated with a Cayley graph $(\Gamma,G)$ of a cancellative monoid $\Gamma$ with a finite…

In 1960 Fuchs posed the problem of characterizing the groups which are the groups of units of commutative rings. In the following years, some partial answers have been given to this question in particular cases. In this paper we address…

In this note we study the constraints on F-theory GUTs with extra $U(1)$'s in the context of elliptic fibrations with rational sections. We consider the simplest case of one abelian factor (Mordell-Weil rank one) and investigate the…

Stressing the role of dual coalgebras, we modify the definition of affine schemes over the 'field with one element'. This clarifies the appearance of Habiro-type rings in the commutative case, and, allows a natural noncommutative…

In this paper we describe the fundamental group-scheme of a proper variety fibered over an abelian variety with rationally connected fibers over an algebraically closed field. We use old and recent results for the Nori fundamental…