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Hoppa till huvudinnehållet
Ikon kryss

Patrik Lundström

Patrik Lundström

Professor

Forskare i algebra

Anställd på Avdelningen för matematik, data och lantmäteri.

Forskar inom naturvetenskap, matematik.


Forskningsintresse/forskningsområde

I min forskning studerar jag egenskaper hos algebraiska system av olika slag. Det finns tre olika huvudinriktningar i min forskning. Den första inriktningen handlar om existens av olika sorters baser för så kallade Galoisutvidgningar. Bland dessa baser kan speciellt nämnas normala baser, primitiva baser och kombinationer av dessa. Den andra inriktningen handlar om svaga topologiseringar av funktorkategorier. Bland dessa finns till exempel topologiska och oskarpa (fuzzy) algebraiska system. Den tredje inriktningen – som jag varit mest aktiv i de senaste åren – handlar om algebraiska system som är utrustade med en så kallad gradering. Frågor som är relevanta för sådana system är vilken kopplingen är mellan enkelhet och graderad enkelhet samt när sådana strukturer är separabla.

Undervisning/handledning

Jag undervisar i matematik i huvudsak inom våra tekniker- och ingenjörsprogram.

Nyckelord

Algebra, ringar, moduler, graderade ringar, category theory, fuzzy mathematics.

Publikationer

Arc length of function graphs via Taylor’s formula

Publicerat

Arc length of function graphs via Taylor’s formula

We use Taylor’s formula with Lagrange remainder to prove that functions with bounded second derivative are rectifiable in the case when polygonal...

DiVA
Von-Neumann Finiteness and Reversibility in some Classes of Non-Associative Algebras

Publicerat

Von-Neumann Finiteness and Reversibility in some Classes of Non-Associative Algebras

We investigate criteria for von-Neumann finiteness and reversibility in some classes of non-associative algebras. Types of algebras that are studie...

DiVA
Epsilon-Strongly Groupoid-Graded Rings, The Picard Inverse Category And Cohomology

Publicerat

Epsilon-Strongly Groupoid-Graded Rings, The Picard Inverse Category And Cohomology

We introduce the class of partially invertible modules and show that it is an inverse category which we call the Picard inverse category. We use th...

DiVA
Group gradations on Leavitt path algebras

Publicerat

Group gradations on Leavitt path algebras

Given a directed graph E and an associative unital ring R one may define the Leavitt path algebra with coefficients in R, denoted by LR(E). For an...

DiVA
Noncommutatively Graded Algebras

Publicerat

Noncommutatively Graded Algebras

Inspired by the commutator and anticommutator algebras derived from algebras graded by groups, we introduce noncommutatively graded algebras. We...

DiVA
Poisson’s fundamental theorem of calculus via Taylor’s formula

Publicerat

Poisson’s fundamental theorem of calculus via Taylor’s formula

We use Taylor’s formula with Lagrange remainder to make a modern adaptation of Poisson’s proof of a version of the fundamental theorem of calculus ...

DiVA
Simple graded rings, nonassociative crossed products and Cayley-Dickson doublings

Publicerat

Simple graded rings, nonassociative crossed products and Cayley-Dickson doublings

e show that if a nonassociative unital ring is graded by a hypercentral group, then the ring is simple if and only if it is graded simple and the...

DiVA
Simplicity of algebras via epsilon-strong systems

Publicerat

Simplicity of algebras via epsilon-strong systems

We obtain sufficient criteria for simplicity of systems, that is, rings R that are equipped with a family of additive subgroups R-s for s is an...

DiVA
Simplicity of Ore monoid rings

Publicerat

Simplicity of Ore monoid rings

Given a non-associative unital ring R, a monoid G and a set π of additive maps R→R, we introduce the Ore monoid ring R[π;G], and, in a special...

DiVA
Artinian and noetherian partial skew groupoid rings

Publicerat

Artinian and noetherian partial skew groupoid rings

Let alpha = {alpha(g) : Rg-1 -> R-g}(g is an element of mor(G)) be a partial action of a groupoid G on a (not necessarily associative) ring R and l...

DiVA
Epsilon-strongly graded rings, separability and semisimplicity

Publicerat

Epsilon-strongly graded rings, separability and semisimplicity

We introduce the class of epsilon-strongly graded rings and show that it properly contains both the class of strongly graded rings and the class of...

DiVA
Non-associative Ore extensions

Publicerat

Non-associative Ore extensions

We introduce non-associative Ore extensions, S = R[X; sigma, delta], for any non-ssociative unital ring R and any additive maps sigma, delta : R ->...

DiVA
Partial category actions on sets and topological spaces

Publicerat

Partial category actions on sets and topological spaces

We introduce (continuous) partial category actions on sets (topological spaces) and show that each such action admits a universal globalization....

DiVA
A proof of the law of sines using the law of cosines

Publicerat

A proof of the law of sines using the law of cosines

We give a proof of the law of sines using the law of cosines. © Mathematical Association of America.

DiVA
Fuzzy crossed product algebras

Publicerat

Fuzzy crossed product algebras

We introduce fuzzy groupoid graded rings and, as a par-ticular case, fuzzy crossed product algebras. We show that there is abijection between the s...

DiVA
Outer Partial Actions and Partial Skew Group Rings

Publicerat

Outer Partial Actions and Partial Skew Group Rings

We extend the classicial notion of an outer action α of a group G on a unital ring A to the case when α is a partial action on ideals, all of which...

DiVA
Simple semigroup graded rings

Publicerat

Simple semigroup graded rings

We show that if R is a, not necessarily unital, ring graded by a semigroup G equipped with an idempotent e such that G is cancellative at e, the...

DiVA
A Proof of the Cosine Addition Formula Using the Law of Cosines

Publicerat

A Proof of the Cosine Addition Formula Using the Law of Cosines

We give a proof of the cosine addition formula using the law of cosines.

DiVA
Simple rings and degree maps

Publicerat

Simple rings and degree maps

For an extension A/B of neither necessarily associative nor necessarily unital rings, we investigate the connection between simplicity of A with a...

DiVA
A combinatorial proof of associativity of Ore extensions

Publicerat

A combinatorial proof of associativity of Ore extensions

We use a counting argument to show that Ore extensions are associative. 

DiVA
Simple skew category algebras associated with minimal partially defined dynamical systems

Publicerat

Simple skew category algebras associated with minimal partially defined dynamical systems

In this article, we continue our study of category dynamical systems, that is functors s from a category G to Topop, and their corresponding skew...

DiVA
Limits of Fuzzy Categories

Publicerat

Limits of Fuzzy Categories

Serving as a generalization of many examples of fuzzy algebraical systems, we introduce fuzzy categories and show that categories formed by fuzzy...

DiVA

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