Finitely Generated Projective modules over exchange rings.
Finitely Presented Modules over Right Non-Singular Rings
Finiteness aspects of Gorenstein homological dimensions
We present an alternative way of measuring the Gorenstein projective (resp., injective) dimension of modules via a new type of complete projective (resp., injective) resolutions. As an application, we easily recover well known theorems such as the Auslander-Bridger formula. Our approach allows us to relate the Gorenstein global dimension of a ring R to the cohomological invariants silp(R) and spli(R) introduced by Gedrich and Gruenberg by proving that leftG-gldim(R) = maxleftsilp(R), leftspli(R),...
Finiteness of local homology modules
Let be an ideal of Noetherian ring and a finitely generated -module. In this paper, we introduce the concept of weakly colaskerian modules and by using this concept, we give some vanishing and finiteness results for local homology modules. Let , we will prove that for any integer
Finiteness of the strong global dimension of radical square zero algebras
The strong global dimension of a finite dimensional algebra A is the maximum of the width of indecomposable bounded differential complexes of finite dimensional projective A-modules. We prove that the strong global dimension of a finite dimensional radical square zero algebra A over an algebraically closed field is finite if and only if A is piecewise hereditary. Moreover, we discuss results concerning the finiteness of the strong global dimension of algebras and the related problem on the density...
Finitistic dimension of artian rings with vanishing radical cube.
Finitistic dimensions of semiprimary rings.
Formality theorems: from associators to a global formulation
Let be a differential manifold. Let be a Drinfeld associator. In this paper we explain how to construct a global formality morphism starting from . More precisely, following Tamarkin’s proof, we construct a Lie homomorphism “up to homotopy" between the Lie algebra of Hochschild cochains on and its cohomology ). This paper is an extended version of a course given 8 - 12 March 2004 on Tamarkin’s works. The reader will find explicit examples, recollections on -structures, explanation of the...
Formules explicites pour le caractère de Chern en -théorie algébrique
Dans cet article on donne une formule explicite pour le caractère de Chern reliant la - théorie algébrique et l’homologie cyclique négative. On calcule le caractère de Chern des symboles de Steinberg et de Loday et on donne une preuve élémentaire du fait que le caractère de Chern est multiplicatif.
FP-injective and weakly quasi-Frobenius rings.
From Poisson algebras to Gerstenhaber algebras
Constructing an even Poisson algebra from a Gerstenhaber algebra by means of an odd derivation of square 0 is shown to be possible in the category of Loday algebras (algebras with a non-skew-symmetric bracket, generalizing the Lie algebras, heretofore called Leibniz algebras in the literature). Such “derived brackets” give rise to Lie brackets on certain quotient spaces, and also on certain Abelian subalgebras. The construction of these derived brackets explains the origin of the Lie bracket on...
Fully idempotent near-rings and sheaf representations.
G-algebras, Jacobson radical and almost split sequences.
Gaussian and Prüfer conditions in bi-amalgamated algebras
Let and be two ring homomorphisms and let and be ideals of and , respectively, such that . In this paper, we investigate the transfer of the notions of Gaussian and Prüfer rings to the bi-amalgamation of with along with respect to (denoted by introduced and studied by S. Kabbaj, K. Louartiti and M. Tamekkante in 2013. Our results recover well known results on amalgamations in C. A. Finocchiaro (2014) and generate new original examples of rings possessing these properties.
Gelfand-Kirillov Dimensions of a Tensor Product.
Generalized adjoint semigroups of a ring.
Generalized SV-modules.
Generalized -rings and von Neumann regular rings
Generalized V-Rings.
Generators of existence varieties of regular rings and complemented Arguesian lattices
We proved in an earlier work that any existence variety of regular algebras is generated by its simple unital Artinian members, while any existence variety of Arguesian sectionally complemented lattices is generated by its simple members of finite length. A characterization of the class of simple unital Artinian members [members of finite length, respectively] of such varieties is given in the present paper.