Related papers: Endomorphism rings via minimal morphisms

This article is concerned with homological properties of local or graded rings whose defining relations are monomials on some regular sequence. The main result of the article positively answers a question of Avramov for such a ring $R$.…

Let $K$ be a field of characteristic zero, $K[x,y]$ be the polynomial ring in two variables. Let $\phi=(f, g)$ be an endomorphism of $K[x,y]$. It is proved that if $\phi$ maps each coordinate to a generator of some proper retract, then it…

A topological monoid is isomorphic to an endomorphism monoid of a countable structure if and only if it is separable and has a compatible complete ultrametric such that composition from the left is non-expansive. We also give a topological…

We derive basic properties of minimal extensions of local rings and their restrictions to subrings. Some applications are included to subrings of truncated polynomial rings.

We give a method for constructing (possible large) self--small modules via some special homomorphisms of rings, called here weak epimorphisms.

We introduce a general notion of depth two for ring homomorphism N --> M, and derive Morita equivalence of the step one and three centralizers, R = C_M(N) and C = End_{N-M}(M \o_N M), via dual bimodules and step two centralizers A =…

Normal endomorphisms of von Neumann algebras need not be extendable to automorphisms of a larger von Neumann algebra, but they always have asymptotic lifts. We describe the structure of endomorphisms and their asymptotic lifts in some…

Let $A$ be a finite dimensional algebra over an algebraically closed field $k$, $\mathcal {D}^b(A)$ be the bounded derived category of $A$-mod and $A^{(m)}$ be the $m$-replicated algebra of $A$. In this paper, we investigate the structure…

An interchange ring,(R,+,*)is an abelian group with a second binary operation defined so that the interchange law (x+y)*(u+v)=(x*u)+(y*v)holds. An interchange near ring is the same structure based on a group which may not be abelian. It is…

Let R be a discrete unital ring, and let M be an R-bimodule. We extend Waldhausen's equivalence from the suspension of the Nil K-theory of R with coefficients in M to the K theory of the tensor algebra T_R(M), and get a map from the…

We determine the geometric structure of a minimal projective threefold having two `independent and commutative' automorphisms of positive topological entropy, and generalize this result to higher-dimensional smooth minimal pairs (X, G). As…

A ring R is called an E-ring if the canonical homomorphism from R to the endomorphism ring End(R_Z) of the additive group R_Z, taking any r in R to the endomorphism left multiplication by r turns out to be an isomorphism of rings. In this…

A characterization of right (left) quasi-duo skew polynomial rings of endomorphism type and skew Laurent polynomial rings are given. In particular, it is shown that (1) the polynomial ring R[x] is right quasi-duo iff R[x] is commutative…

Given a subdirectly irreducible *-regular ring R, we show that R is a homomorphic image of a regular *-subring of an ultraproduct of the (simple) eRe, e in the minimal ideal of R. Moreover, unit-regularity is shown for every member of the…

We prove that a local ring $R$ of embedding codepth at most 3 has at most two semidualizing complexes up to shift-isomorphism, namely, $R$ itself and a dualizing $R$-complex if one exists.

Let $i: \mathrm{L} \hookrightarrow \mathrm{X}$ be a compact K\"{a}hler Lagrangian in a holomorphic symplectic variety $\mathrm{X}/\mathbf{C}$. We use deformation quantisation to show that the endomorphism differential graded algebra…

The Mordell-Lang conjecture describes the intersection of a finitely generated subgroup with a closed subvariety of a semiabelian variety. Equivalently, this conjecture describes the intersection of closed subvarieties with the set of…

We investigate equidecomposability in the ring of polygons with sides restricted to given directions and using only translations. Extending classical results of Dehn and Hadwiger, we prove that equidecomposability in these rings is…

In algebraic quantum field theory we consider nets of von Neumann algebras indexed over regions of the space-time. Wiesbrock has shown that strongly additive nets of von Neumann algebras on the circle are in correspondence with standard…

Let $V=V_1 \otimes \cdots \otimes V_n$ be a vector space over an algebraically closed field $K$ of characteristic zero with $\dim(V_i)=d_i$. We study the ring of polynomial invariants $K[\operatorname{End}(V)^{\oplus…