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A note about anti-derivations on the Exterior modules

Year 2022, , 380 - 384, 15.01.2022
https://doi.org/10.17714/gumusfenbil.906177

Abstract

Modules are a subject that has been worked on in Commutative Algebra. The most known types of these modules are the Exterior Modules and Symmetricl modules. This study will examine the inverse derivatives of finite produced Exterior modules on any R-ring with zero characteristics and some of the features of these modules. In addition, the stable sub-modules of the Exterior module on the same R-ring have been examined. Some results are given on the inverse derivatives of these stable submodule structures.

References

  • Baer, R. (1952). Linear algebra & Projective geometry. (1st ed.). New York: Academic Press Inc.
  • Bland, P.E. (2005). Higher derivations on rings & Modules. International Journal of Mathematics and Mathematical Sciences, 263497, https://doi.org/10.1155/IJMMS.2005.2373.
  • Bracic, J. (2001). Representations & Derivations of modules. Irish Mathematical Society Bulletin, 47(2001), 27-39.
  • Çagman, A. (2017). Explicit Gröbner basis of the ideal of vanishing polynomials over Z_2 xZ_2. Karaelmas Fen Mühendislik Dergisi, 7(2), 349-351.
  • Grothendieck, A. (1967). Elements de geometrie algebrique. publicationes mathematicae. (Vol. 4). I.H.E.S: Paris.
  • Hart, R. (1996). Higher derivations & Universal differentials operators. Journal of Algebra, 0253, 184, 175- 181. https://doi.org/10.1006/jabr.1996.0253.
  • Hoffman, K., & Kunze, R. (1961). Linear algebra. (2nd ed.). Englewood Cliffs, New Jersey: Prentice-Hall Inc.
  • Karakuş, A. (2021). An approximation to second exterior derivation of high order universal modules, Algebra Letters, 1(2021), 1-13.
  • Kuiper, N. (1961). Linear algebra & Geometry. (1st ed.). North-Holland Publishing Company.
  • Matsumura, H. (1986). Commutative ring theory. (1st ed.). Cambridge, UK: Cambridge University Press.
  • Osborn, H. (1968). Module of differentials II. Mathematische Annalen, 175, 146-158.
  • Polat, K., & Çagman, A. (2021). Polcag spaces: I. group-like structures. Thai Journal of Mathematics, 19(1), 87-92.
  • Rim, S.H. (1987). Extensions of high anti-derivations to modules of quotients. Journal of the Korean Mathematical Society,24(1), 25-31.

Exterior modüller üzerinde ters türevler hakkında bir not

Year 2022, , 380 - 384, 15.01.2022
https://doi.org/10.17714/gumusfenbil.906177

Abstract

Modüller Değişmeli Cebir’de üzerinde çokça çalışılan bir konudur. Bu modüllerin en bilinen türleri Exterior Modüller ve Simetrik Modüllerdir. Bu çalışmada, karakteristiği sıfır olan herhangi bir R halkası üzerindeki sonlu üretilmiş Exterior modüllerin ters türevleri ve bu modüllerin bazı özellikleri incelenecektir. Ayrıca, aynı R halkası üzerindeki Exterior modülün kararlı alt modülleri incelenmiştir. Bu kararlı alt modül yapılarının ters türevleri hakkında elde edilen bazı sonuçlar verilmiştir.

References

  • Baer, R. (1952). Linear algebra & Projective geometry. (1st ed.). New York: Academic Press Inc.
  • Bland, P.E. (2005). Higher derivations on rings & Modules. International Journal of Mathematics and Mathematical Sciences, 263497, https://doi.org/10.1155/IJMMS.2005.2373.
  • Bracic, J. (2001). Representations & Derivations of modules. Irish Mathematical Society Bulletin, 47(2001), 27-39.
  • Çagman, A. (2017). Explicit Gröbner basis of the ideal of vanishing polynomials over Z_2 xZ_2. Karaelmas Fen Mühendislik Dergisi, 7(2), 349-351.
  • Grothendieck, A. (1967). Elements de geometrie algebrique. publicationes mathematicae. (Vol. 4). I.H.E.S: Paris.
  • Hart, R. (1996). Higher derivations & Universal differentials operators. Journal of Algebra, 0253, 184, 175- 181. https://doi.org/10.1006/jabr.1996.0253.
  • Hoffman, K., & Kunze, R. (1961). Linear algebra. (2nd ed.). Englewood Cliffs, New Jersey: Prentice-Hall Inc.
  • Karakuş, A. (2021). An approximation to second exterior derivation of high order universal modules, Algebra Letters, 1(2021), 1-13.
  • Kuiper, N. (1961). Linear algebra & Geometry. (1st ed.). North-Holland Publishing Company.
  • Matsumura, H. (1986). Commutative ring theory. (1st ed.). Cambridge, UK: Cambridge University Press.
  • Osborn, H. (1968). Module of differentials II. Mathematische Annalen, 175, 146-158.
  • Polat, K., & Çagman, A. (2021). Polcag spaces: I. group-like structures. Thai Journal of Mathematics, 19(1), 87-92.
  • Rim, S.H. (1987). Extensions of high anti-derivations to modules of quotients. Journal of the Korean Mathematical Society,24(1), 25-31.
There are 13 citations in total.

Details

Primary Language Turkish
Subjects Engineering
Journal Section Articles
Authors

Ali Karakuş 0000-0002-8483-0137

Publication Date January 15, 2022
Submission Date March 30, 2021
Acceptance Date January 1, 2022
Published in Issue Year 2022

Cite

APA Karakuş, A. (2022). Exterior modüller üzerinde ters türevler hakkında bir not. Gümüşhane Üniversitesi Fen Bilimleri Dergisi, 12(1), 380-384. https://doi.org/10.17714/gumusfenbil.906177