Related papers: Effective codescent morphisms in some varieties of…
We show that a class of algebras is closed under the taking of homomorphic images and direct products if and only if the class consists of all algebras that satisfy a set of (generally simultaneous) equations. For classes of regular…
We introduce the notion of being cohomologically complete for objects of the derived category of sheaves of $Z[\hbar]$-modules on a topological space. Then we consider a $Z[\hbar]$-algebra satisfying some suitable conditions and prove…
In this work, we obtain contraction results for a class of diagrams of ring morphisms which strictly includes the ones obtained by Lipman. Further, we present some applications on quotient and in the changing of the base ring in the…
We prove that if A is a finite algebra with a parallelogram term that satisfies the split centralizer condition, then A is dualizable. This yields yet another proof of the dualizability of any finite algebra with a near unanimity term, but…
It is shown that, in the variety of ternary rings, the elements of amalgamated free products have unique normal forms, and, moreover, this variety satisfies the strong amalgamation property. Applying these statements, effective codescent…
Assume that two algebraic varieties of finite type over the complex numbers are related by a morphism whose fibers are precisely the orbits for the action of a unipotent group. We show that the two varieties have the same topological Euler…
In this note, we show a uniqueness result of homogeneous quasimorphisms defined on the universal cover of the symplectic linear group.
We categorify cocompleteness results of monad theory, in the context of pseudomonads. We first prove a general result establishing that, in any 2-category, weighted bicolimits can be constructed from oplax bicolimits and bicoequalizers of…
We investigate the representation and complete representation classes for algebras of partial functions with the signature of relative complement and domain restriction. We provide and prove the correctness of a finite equational…
Given a group satisfying sufficient finiteness properties, we discuss a group algebra criterion for vanishing of all its cohomology groups with unitary coefficients in a certain degree.
An abstract mathematical framework is presented in this paper as a unification of several deformed or generalized algebra proposed recently in the context of generalized statistical theories intended to treat certain complex thermodynamic…
We give a valuative criterion for when a smooth algebraic stack with a separated good moduli space is the quotient of a separated Deligne-Mumford stack by a torus. For doing so, we introduce a new class of morphisms, the so-called effective…
We prove new necessary and sufficient conditions for a morphism of coalgebras to be a monomorphism, different from the ones already available in the literature. More precisely, $\phi: C \to D$ is a monomorphism of coalgebras if and only if…
Yet another proof of the result asserting that a morphism of commutative rings is an effective descent morphism for modules if and only if it is pure is given. Moreover, it is shown that this result cannot be derived from Moerdijk's descent…
It is proved that the derivation algebra of a centerless perfect Lie algebra of arbitrary dimension over any field of arbitrary characteristic is complete and that the holomorph of a centerless perfect Lie algebra is complete if and only if…
A characterization of the general linear equation in standard form admitting a maximal symmetry algebra is obtained in terms of a simple set of conditions relating the coefficients of the equation. As a consequence, it is shown that in its…
We give some sufficient conditions for the injectivity of actions of compact quantum groups on $C^{\ast}$-algebra. As an application, we prove that any faithful smooth action by a compact quantum group on a compact smooth (not necessarily…
Last years a number of papers were devoted to describing automorphisms of semigroups of endomorphisms of free finitely generated universal algebras of some varieties: groups, semigroups, associative commutative algebras, inverse semigroups,…
We characterize universally generalizing morphisms which satisfy descent of algebraic cycles integrally as those universally generalizing morphisms which are surjective with generically reduced fibres. In doing so, we introduce a naive…
We say that there is a representation of the universal algebra B in the universal algebra A if the set of endomorphisms of the universal algebra A has the structure of universal algebra B. Therefore, the role of representation of the…