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Dive into the research topics where Jeremy Haefner is active.

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Featured researches published by Jeremy Haefner.


Journal of Algebra | 1995

Graded equivalence theory with applications

Jeremy Haefner

We develop the foundations for graded equivalence theory and apply them to investigate properties such as primeness, finite representation type, and vertex theory of graded rings. The key fact that we prove is that, for any two G-graded rings R and S such that there is a category equivalence from gr(R) to gr(S) that commutes with suspensions, then, for any subgroup H of G, the categories gr(H|G,R) and gr(H|G,S) of modules graded by the G-set of right cosets are also equivalent.


Proceedings of the American Mathematical Society | 1997

Isomorphisms of row and column finite matrix rings

Jeremy Haefner; Á. del Río; Juan Jacobo Simón

First published in Proceedings of the American Mathematical Society in vol. 125, no. 6, published by the American Mathematical Society.


Transactions of the American Mathematical Society | 2000

Hereditary crossed products

Jeremy Haefner; Gerald J. Janusz

First published in Transactions of the American Mathematical Society in vol. 352, no. 7, published by the American Mathematical Society.


Acta Mathematica Hungarica | 1999

Approximating Rings with Local Units Via Automorphisms

Gene Abrams; Jeremy Haefner; Á. del Río

For a ring A with local units we investigate unital overrings T of A, and compare the automorphism groups Aut (A) and Aut (T).


Transactions of the American Mathematical Society | 1998

Picard groups and infinite matrix rings

Gene Abrams; Jeremy Haefner

We describe a connection between the Picard group of a ring with local units T and the Picard group of the unital overring End(TT). Using this connection, we show that the three groups Pic(R), Pic(FM(R)), and Pic(RFM(R)) are isomorphic for any unital ring R. Furthermore, eaclh ele- ment of Pic(RFM(R)) arises from an automorphism of RFM(R), which yields an isomorphsm between Pic(RFM(R)) and Out(RFM(R)). As one applica- tion we extend a classical result of Rosenberg and Zelinsky by showing that the group OutR(RFM(R)) is abelian for any commutative unital ring R.


Communications in Algebra | 2001

STRONGLY GRADED HEREDITARY ORDERS

Jeremy Haefner; Christopher J. Pappacena

Let R be a Dedekind domain with global quotient field K. The purpose of this note is to provide a characterization of when a strongly graded R-order with semiprime 1-component is hereditary. This generalizes earlier work by the first author and G. Janusz in (J. Haefner and G. Janusz, Hereditary crossed products, Trans. Amer. Math. Soc. 352 (2000), 3381–3410). *This work was supported in part by a Baylor University Research Grant.


Transactions of the American Mathematical Society | 1990

Local orders whose lattices are direct sums of ideals

Jeremy Haefner

First published in Transactions of the American Mathematical Society in vol. 321, no. 2, published by the American Mathematical Society.


Communications in Algebra | 1994

A strongly graded ring that is

Jeremy Haefner

We construct a ring that is strongly graded by the integers such that it is not graded equivalent to a skew group ring. This is in contrast to the finite case and the results of Cohen and Montgomery, in which every strongly graded ring is graded equivalent to a skew group ring 2


Journal of Algebra | 1991

On local orders

Jeremy Haefner

Abstract Let R be a complete local Dedekind domain with quotient field K and let Λ be a local R -order in a separable K -algebra. This paper has two major goals. The first is to describe the local orders such that every uniform R -torsion-free module is tame. The second is to describe the pullback structure of local orders with finite representation type and such that every uniform R -torsion-free module is tame. We acomplish these goals by constructing an “ n -ad” order which is, in a certain sense, a maximal local order. This n -ad order provides new characterizations for finite type.


Linear Algebra and its Applications | 2000

The Picard group of a structural matrix algebra

Jeremy Haefner; Trae Holcomb

Abstract We investigate the Picard group of a structural matrix (or incidence) algebra A of a finite preordered set P over a field and we consider five interrelated problems. Our main technique involves establishing a connection between the group of outer automorphisms Out( A ) of A and the group of outer automorphisms of the basic algebra A which is an incidence algebra of the associated partially ordered set P of P . We discuss necessary and sufficient conditions for Out( A ) to be a natural invariant for the Morita equivalence class of A , and necessary and sufficient conditions for M n ( K ) to be strongly graded by a group G and coefficient ring A containing n primitive, orthogonal idempotents.

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Gene Abrams

University of Colorado Colorado Springs

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Kulumani M. Rangaswamy

University of Colorado Colorado Springs

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Trae Holcomb

United States Air Force Academy

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