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Cellular covers of cotorsion-free modules

Rüdiger Göbel, José L. Rodríguez, Lutz Strüngmann (2012)

Fundamenta Mathematicae

In this paper we improve recent results dealing with cellular covers of R-modules. Cellular covers (sometimes called colocalizations) come up in the context of homotopical localization of topological spaces. They are related to idempotent cotriples, idempotent comonads or coreflectors in category theory. Recall that a homomorphism of R-modules π: G → H is called a cellular cover over H if π induces an isomorphism π : H o m R ( G , G ) H o m R ( G , H ) , where π⁎(φ) = πφ for each φ H o m R ( G , G ) (where maps are acting on the left). On the one hand,...

Faithfully quadratic rings - a summary of results

M. Dickmann, F. Miraglia (2016)

Banach Center Publications

This is a summary of some of the main results in the monograph Faithfully Ordered Rings (Mem. Amer. Math. Soc. 2015), presented by the first author at the ALANT conference, Będlewo, Poland, June 8-13, 2014. The notions involved and the results are stated in detail, the techniques employed briefly outlined, but proofs are omitted. We focus on those aspects of the cited monograph concerning (diagonal) quadratic forms over preordered rings.

On a -Kasch spaces

Ali Akbar Estaji, Melvin Henriksen (2010)

Archivum Mathematicum

If X is a Tychonoff space, C ( X ) its ring of real-valued continuous functions. In this paper, we study non-essential ideals in C ( X ) . Let a be a infinite cardinal, then X is called a -Kasch (resp. a ¯ -Kasch) space if given any ideal (resp. z -ideal) I with gen ( I ) < a then I is a non-essential ideal. We show that X is an 0 -Kasch space if and only if X is an almost P -space and X is an 1 -Kasch space if and only if X is a pseudocompact and almost P -space. Let C F ( X ) denote the socle of C ( X ) . For a topological space X with only...

On structure space of Γ -semigroups

S. Chattopadhyay, S. Kar (2008)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

In this paper we introduce the notion of the structure space of Γ -semigroups formed by the class of uniformly strongly prime ideals. We also study separation axioms and compactness property in this structure space.

Ordinary selfdistributive rings

Sobhy Ghoneim, Marian Kechlibar, Tomáš Kepka (2005)

Commentationes Mathematicae Universitatis Carolinae

Left selfdistributive rings (i.e., x y z = x y x z ) which are semidirect sums of boolean rings and rings nilpotent of index at most 3 are studied.

Quantum sections and Gauge algebras.

Lieven Le Bruyn, Freddy van Oystaeyen (1992)

Publicacions Matemàtiques

Using quantum sections of filtered rings and the associated Rees rings one can lift the scheme structure on Proj of the associated graded ring to the Proj of the Rees ring. The algebras of interest here are positively filtered rings having a non-commutative regular quadratic algebra for the associated graded ring; these are the so-called gauge algebras obtaining their name from special examples appearing in E. Witten's gauge theories. The paper surveys basic definitions and properties but concentrates...

The symplectic Gram-Schmidt theorem and fundamental geometries for 𝒜 -modules

Patrice P. Ntumba (2012)

Czechoslovak Mathematical Journal

Like the classical Gram-Schmidt theorem for symplectic vector spaces, the sheaf-theoretic version (in which the coefficient algebra sheaf 𝒜 is appropriately chosen) shows that symplectic 𝒜 -morphisms on free 𝒜 -modules of finite rank, defined on a topological space X , induce canonical bases (Theorem 1.1), called symplectic bases. Moreover (Theorem 2.1), if ( , φ ) is an 𝒜 -module (with respect to a -algebra sheaf 𝒜 without zero divisors) equipped with an orthosymmetric 𝒜 -morphism, we show, like in the classical...

Uniform filters

Manuel Garcia Román, Mercedes Márquez Hernández, Pascual Jara, Alain Verschoren (1999)

Cahiers de Topologie et Géométrie Différentielle Catégoriques

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