Related papers: The structure of corings with a grouplike element

We consider the class of all commutative reduced rings for which there exists a finite subset T of A such that all projections on quotients by prime ideals of A are surjective when restricted to T. A complete structure theorem is given for…

We show that the category of corings over a fixed base ring with local units is equivalent to the category of comonads in (right) unital modules whose underlying functors preserve inductive limits. Changing base rings, we prove a…

The paper provides a computation of the additive structure as well as a partial description of the Chern-class module structure of the cohomology of $GL_3$ over the function ring of an elliptic curve over a finite field. The computation is…

Let $R$ be a commutative noetherian ring. The $n$-semidualizing modules of $R$ are generalizations of its semidualizing modules. We will prove some basic properties of $n$-semidualizing modules. Our main result and example shows that the…

Structural properties of unitary groups over local, not necessarily commutative, rings are developed, with applications to the computation of the orders of these groups (when finite) and to the degrees of the irreducible constituents of the…

In this paper, we attempt to develop the Quillen Suslin theory for the algebraic fundamental group of a ring. We give a surjective group homomorphism from the algebraic fundamental group of the field of the real numbers to the group of…

This paper investigates coherent-like conditions and related properties that a trivial extension might inherit from the ground ring over some classes of modules. It captures previous results dealing primarily with coherence, and also…

This survey article explores the notion of z-classes in groups. The concept introduced here is related to the notion of orbit types in transformation groups, and types or genus in the representation theory of finite groups of Lie type. Two…

A relationship between coseparable corings and separable non-unital rings is established. In particular it is shown that an A-coring C has an associative A-balanced product. A Morita context is constructed for a coseparable coring with a…

We focus our attention to the set $\gl{\coring{C}}$ of grouplike elements of a coring $\coring{C}$ over a ring $A$. We do some observations on the actions of the groups $U(A)$ and $\aut{\coring{C}}$ of units of $A$ and of automorphisms of…

Prime objects were defined as generalization of simple objects in the categories of rings (modules). In this paper we introduce and investigate what turns out to be a suitable generalization of simple corings (simple comodules), namely…

We describe how some aspects of abstract localization on module categories have applications to the study of injective comodules over some special types of corings. We specialize the general results to the case of Doi-Koppinen modules,…

Galois comodules of a coring are studied. The conditions for a simple comodule to be a Galois comodule are found. A special class of Galois comodules termed principal comodules is introduced. These are defined as Galois comodules that are…

We construct a ring structure on complex cobordism tensored with the rationals, which is related to the usual ring structure as quantum cohomology is related to ordinary cohomology. The resulting object defines a generalized two-…

A model structure on the category of (small) bigroupoids and pseudofunctors is constructed. In this model structure, every object is cofibrant. In order to keep certain calculations of manageable size, a coherence theorem for bigroupoids…

The Chern-Galois theory is developed for corings or coalgebras over non-commutative rings. As the first step the notion of an entwined extension as an extension of algebras within a bijective entwining structure over a non-commutative ring…

Let $R$ by a right coherent ring and $R$-Mod denote the category of left $R$-modules. We show that there is an abelian model structure on $R$-Mod whose cofibrant objects are precisely the Gorenstein flat modules. Employing a new method for…

This paper introduces the category of marked curved Lie algebras with curved morphisms, equipping it with a closed model category structure. This model structure is---when working over an algebraically closed field of characteristic…

In this paper, we introduce homological structure theory of semirings and CP-semirings---semirings all of whose cyclic semimodules are projective. We completely describe semisimple, Gelfand, subtractive, and anti-bounded, CP-semirings. We…

An important example of a model category is the category of unbounded chain complexes of R-modules, which has as its homotopy category the derived category of the ring R. This example shows that traditional homological algebra is…