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Lundström, P. (2023). Algebra, trigonometri och analys (1ed.). Lund: Studentlitteratur AB
Open this publication in new window or tab >>Algebra, trigonometri och analys
2023 (Swedish)Book (Other academic)
Place, publisher, year, edition, pages
Lund: Studentlitteratur AB, 2023. p. 649 Edition: 1
Keywords
Algebra, Trigonometry, Algebra, Trigonometri, Analytisk trigonometri
National Category
Algebra and Logic
Identifiers
urn:nbn:se:hv:diva-21051 (URN)9789144166421 (ISBN)
Available from: 2023-12-11 Created: 2023-12-11 Last updated: 2024-01-03Bibliographically approved
Lundström, P. & Öinert, J. (2023). Corrigendum: Group gradations on Leavitt path algebras. Journal of Algebra and its Applications
Open this publication in new window or tab >>Corrigendum: Group gradations on Leavitt path algebras
2023 (English)In: Journal of Algebra and its Applications, ISSN 0219-4988, E-ISSN 1793-6829Article in journal (Other academic) Published
Abstract [en]

The results that are stated in P. Nystedt and J. Öinert [Group gradations on Leavitt path algebras, J. Algebra Appl. 19(9) (2020) 2050165, Sec. 4] hold true, but due to an oversimplification some of the proofs are incomplete. The purpose of this note is to amend and complete the affected proofs.

Place, publisher, year, edition, pages
World Scientific, 2023
National Category
Algebra and Logic
Identifiers
urn:nbn:se:hv:diva-19880 (URN)10.1142/S0219498824920014 (DOI)000946343400001 ()2-s2.0-85150800283 (Scopus ID)
Available from: 2023-04-24 Created: 2023-04-24 Last updated: 2024-04-12Bibliographically approved
Lundström, P. (2023). Double Calculus. Surveys in Mathematics and its Applications, 18, 27-48
Open this publication in new window or tab >>Double Calculus
2023 (English)In: Surveys in Mathematics and its Applications, ISSN 1843-7265, E-ISSN 1842-6298, Vol. 18, p. 27-48Article in journal (Refereed) Published
Abstract [en]

We present a streamlined, slightly modified version, in the two-variable situation, of a beautiful, but not so well known, theory by Bögel [1, 2], already from the 1930s, on an alternative higher dimensional calculus of real functions, a double calculus, which includes many two-variable extensions of classical results from single variable calculus, such as Rolle’s theorem, Lagrange’s mean value theorem, Cauchy’s mean value theorem, Fermat’s extremum theorem, the first derivative test, and the first and second fundamental theorems of calculus. 

Keywords
continuous function; differentiable function; Riemann integral; the fundamental theorem of calculus
National Category
Mathematical Analysis
Identifiers
urn:nbn:se:hv:diva-20894 (URN)2-s2.0-85173464276 (Scopus ID)
Note

CC BY 4.0

Available from: 2023-12-28 Created: 2023-12-28 Last updated: 2023-12-28
Lundström, P. & Oinert, J. (2023). Group gradations on Leavitt path algebras (vol 19, 2050165, 2020). Journal of Algebra and its Applications, Article ID 2492001.
Open this publication in new window or tab >>Group gradations on Leavitt path algebras (vol 19, 2050165, 2020)
2023 (English)In: Journal of Algebra and its Applications, ISSN 0219-4988, E-ISSN 1793-6829, article id 2492001Article in journal (Refereed) Published
Abstract [en]

The results that are stated in P. Nystedt and J. Oinert [Group gradations on Leavitt path algebras, J. Algebra Appl. 19(9) (2020) 2050165, Sec. 4] hold true, but due to an oversimplification some of the proofs are incomplete. The purpose of this note is to amend and complete the affected proofs.

Place, publisher, year, edition, pages
World Scientific, 2023
Keywords
s-unital ring; strongly graded ring; epsilon-strongly graded ring; Leavitt path algebra
National Category
Algebra and Logic
Identifiers
urn:nbn:se:hv:diva-19847 (URN)10.1142/S0219498824920014 (DOI)000946343400001 ()2-s2.0-85150800283 (Scopus ID)
Available from: 2023-12-20 Created: 2023-12-20 Last updated: 2024-04-29Bibliographically approved
Lundström, P., Öinert, J. & Richter, J. (2023). Non-Unital Ore Extensions. Colloquium Mathematicum, 172(2), 217-229
Open this publication in new window or tab >>Non-Unital Ore Extensions
2023 (English)In: Colloquium Mathematicum, ISSN 0010-1354, E-ISSN 1730-6302, Vol. 172, no 2, p. 217-229Article in journal (Refereed) Published
Abstract [en]

We study Ore extensions of non-unital associative rings. We provide a characterization of simple non-unital differential polynomial rings R[x; delta], under the hy-pothesis that R is s-unital and ker(delta) contains a non-zero idempotent. This result gener-alizes a result by oinert, Richter and Silvestrov from the unital setting. We also present a family of examples of simple non-unital differential polynomial rings.

Keywords
non-unital ring, Ore extension, simple ring, outer derivation
National Category
Algebra and Logic
Identifiers
urn:nbn:se:hv:diva-20692 (URN)10.4064/cm8941-11-2022 (DOI)000917921400001 ()2-s2.0-85163993902 (Scopus ID)
Available from: 2023-09-06 Created: 2023-09-06 Last updated: 2024-01-12Bibliographically approved
Lundström, P. & Öinert, J. (2023). Simplicity of Leavitt Path Algebras via Graded Ring Theory. Bulletin of the Australian Mathematical Society, 108(3), 428-437
Open this publication in new window or tab >>Simplicity of Leavitt Path Algebras via Graded Ring Theory
2023 (English)In: Bulletin of the Australian Mathematical Society, ISSN 0004-9727, E-ISSN 1755-1633, Vol. 108, no 3, p. 428-437Article in journal (Refereed) Published
Abstract [en]

Suppose that R is an associative unital ring and that E= (E-0, E-1, r, s) is a directed graph. Using results from graded ring theory, we show that the associated Leavitt path algebra L-R(E) is simple if and only if R is simple, E-0 has no nontrivial hereditary and saturated subset, and every cycle in E has an exit. We also give a complete description of the centre of a simple Leavitt path algebra.

Place, publisher, year, edition, pages
Cambridge University Press, 2023
Keywords
Leavitt path algebra; graded ring; simple ring; centre
National Category
Algebra and Logic
Identifiers
urn:nbn:se:hv:diva-19848 (URN)10.1017/S0004972723000114 (DOI)000943276000001 ()2-s2.0-85177820296 (Scopus ID)
Note

CC-BY 4.0

Available from: 2023-12-20 Created: 2023-12-20 Last updated: 2023-12-20
Lundström, P. (2022). Primitives of continuous functions via polynomials. International Journal of Mathematical Education in Science and Technology, 1-5
Open this publication in new window or tab >>Primitives of continuous functions via polynomials
2022 (English)In: International Journal of Mathematical Education in Science and Technology, ISSN 0020-739X, E-ISSN 1464-5211, p. 1-5Article in journal (Refereed) Published
Abstract [en]

In standard books on calculus the existence of primitive functions of continuous functions is proved, in one way or another, using Riemann sums. In this note we present a completely different self-contained, however probably folkloristic, proof of this existence. Our proof combines, on the one hand, the so-called Stone Weierstrass theorem on uniform approximation of continuous functions on the unit interval by polynomials, and, on the other hand, a classical result from calculus on the existence of limits of differentiated sequences of functions. The sought for primitive is then constructed as the limit of primitives of the polynomials approximating the original function.

Place, publisher, year, edition, pages
Taylor & Francis Group, 2022
Keywords
Primitive function; integral; polynomial
National Category
Mathematical Analysis
Identifiers
urn:nbn:se:hv:diva-19316 (URN)10.1080/0020739X.2022.2129499 (DOI)000867511300001 ()2-s2.0-85139849437 (Scopus ID)
Available from: 2022-10-28 Created: 2022-10-28 Last updated: 2024-03-21Bibliographically approved
Nystedt, P. (2021). Arc length of function graphs via Taylor’s formula. International Journal of Mathematical Education in Science and Technology, 52(2), 310-323
Open this publication in new window or tab >>Arc length of function graphs via Taylor’s formula
2021 (English)In: International Journal of Mathematical Education in Science and Technology, ISSN 0020-739X, E-ISSN 1464-5211, Vol. 52, no 2, p. 310-323Article in journal (Refereed) Published
Abstract [en]

We use Taylor’s formula with Lagrange remainder to prove that functions with bounded second derivative are rectifiable in the case when polygonal paths are defined by interval subdivisions which are equally spaced. As a means for generating interesting examples of exact arc length calculations in calculus courses, we recall two large classes of functions f with the property that (Formula presented.) has a primitive, including classical examples by Neile, van Heuraet and Fermat, as well as more recent ones induced by Pythagorean triples of functions. We also discuss potential benefits for our proposed definition of arc length in introductory calculus courses. © 2020, © 2020 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group.

Keywords
Taylor's formula, the fundamental theorem of calculus, Riemann sums, arc length
National Category
Mathematical Analysis
Research subject
ENGINEERING, Mathematics
Identifiers
urn:nbn:se:hv:diva-15157 (URN)10.1080/0020739X.2020.1751320 (DOI)000527605900001 ()2-s2.0-85083643127 (Scopus ID)
Available from: 2020-05-04 Created: 2020-05-04 Last updated: 2022-01-19Bibliographically approved
Lundström, P. (2021). Elementär optimeringslära. Lund: Studentlitteratur AB
Open this publication in new window or tab >>Elementär optimeringslära
2021 (Swedish)Book (Other academic)
Abstract [sv]

Elementär optimeringslära inleds med en repetition av grundläggande matematikkunskaper om algebra, ekvationer, matriser, funktioner och derivata. Därefter behandlas linjär optimering, först i två variabler med fokus på geometrisk förståelse och därefter, i det allmänna fallet, med simplexmetoden. Denna metod tillämpas i boken även inom det spännande matematikområdet spelteori. Boken redogör för olika metoder för optimering av allmänna tvåvariabelfunktioner, dels över kompakta områden, dels med Lagranges sats givet ett bivillkor och dels med Hessianen. Boken tar avslutningsvis upp optimering på grafer med Kruskals, Prims och Dijkstras algoritmer.

Place, publisher, year, edition, pages
Lund: Studentlitteratur AB, 2021. p. 331
Keywords
Mathematical optimization, Optimering
National Category
Mathematics Educational Sciences
Identifiers
urn:nbn:se:hv:diva-16608 (URN)9789144141855 (ISBN)
Available from: 2021-07-07 Created: 2021-07-07 Last updated: 2021-07-07Bibliographically approved
Cala, J., Lundström, P. & Pinedo, H. (2021). Graded modules over object-unital groupoid graded rings. Communications in Algebra, 50(2), 444-462
Open this publication in new window or tab >>Graded modules over object-unital groupoid graded rings
2021 (English)In: Communications in Algebra, ISSN 0092-7872, E-ISSN 1532-4125, Vol. 50, no 2, p. 444-462Article in journal (Refereed) Published
Abstract [en]

In this article, we analyze the category(Formula presented) of unitary G-graded modules over object unital G -graded rings R, being G a groupoid. Here we consider the forgetful functor  G - R- mod and determine many properties (Formula presented.) for which the following implications are valid for modules M in (Formula presented.) M is (Formula presented.) (Formula presented.) U(M) is (Formula presented.) U(M) is (Formula presented.) (Formula presented.) M is (Formula presented.) We treat the cases when (Formula presented.) is any of the properties: direct summand, projective, injective, free and semisimple. Moreover, graded versions of results concerning classical module theory are established, as well as some structural properties (Formula presented.). 

Place, publisher, year, edition, pages
Taylor & Francis Group, 2021
Keywords
finitely gererated, finitely presented, free, groupoid graded module, injective, projective, pure sequences, small and flat modules, 16D10, 16D40, 16D50, 16D90
National Category
Algebra and Logic
Identifiers
urn:nbn:se:hv:diva-17455 (URN)10.1080/00927872.2021.1959601 (DOI)000686088500001 ()2-s2.0-85113240292 (Scopus ID)
Note

To see the correct formulas in the abstract; see the original article.

Available from: 2021-11-08 Created: 2021-11-08 Last updated: 2022-04-04Bibliographically approved
Organisations
Identifiers
ORCID iD: ORCID iD iconorcid.org/0000-0001-6594-7041

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