Geodesic
Affine Near-Rings and Related Structures
Matematičeskie zametki, Tome 103 (2018) no. 6, pp. 936-947.

Voir la notice de l'article provenant de la source Math-Net.Ru

Affine near-rings, categories of modules over affine near-rings, and objects associated with them are studied.
Keywords: near-ring, category, functor, equivalence of categories.
Mots-clés : module 
@article{MZM_2018_103_6_a11,
     author = {K.-T. Howell and D. S. Chistyakov},
     title = {Affine {Near-Rings} and {Related} {Structures}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {936--947},
     publisher = {mathdoc},
     volume = {103},
     number = {6},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2018_103_6_a11/}
}
TY  - JOUR
AU  - K.-T. Howell
AU  - D. S. Chistyakov
TI  - Affine Near-Rings and Related Structures
JO  - Matematičeskie zametki
PY  - 2018
SP  - 936
EP  - 947
VL  - 103
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2018_103_6_a11/
LA  - ru
ID  - MZM_2018_103_6_a11
ER  - 
%0 Journal Article
%A K.-T. Howell
%A D. S. Chistyakov
%T Affine Near-Rings and Related Structures
%J Matematičeskie zametki
%D 2018
%P 936-947
%V 103
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2018_103_6_a11/
%G ru
%F MZM_2018_103_6_a11
K.-T. Howell; D. S. Chistyakov. Affine Near-Rings and Related Structures. Matematičeskie zametki, Tome 103 (2018) no. 6, pp. 936-947. http://geodesic.mathdoc.fr/item/MZM_2018_103_6_a11/

[1] H. Bass, Algebraic $K$-Theory, W. A. Benjamin, New York, 1968 | MR | Zbl

[2] A. V. Zhozhikashvili, “Ob ekvivalentnosti kategorii affinnykh modulei”, Matem. zametki, 24:4 (1978), 475–486 | MR | Zbl

[3] P. A. Krylov, “Afinnye gruppy modulei i ikh avtomorfizmy”, Algebra i logika, 40:1 (2001), 60–82 | MR | Zbl

[4] R. Netzsch, “Charakterisierung der affinen Geometrien durch ein kategorientheoretisches Axiomsystem”, Manuscripta Math., 4 (1971), 305–317 | MR

[5] F. Ostermann, J. Schmidt, “Der baryzentrische Kalkül als axiomatische Grundlage der affinen Geometrie”, J. Reine Angew. Math., 224 (1966), 44–57 | MR | Zbl

[6] I. S. Safuanov, “Affinnye kategorii”, UMN, 38:5 (233) (1983), 205–206 | MR | Zbl

[7] I. S. Safuanov, “Affinnye kategorii i kategorii affinny modulei”, Abelevy gruppy i moduli, 8 (1986), 118–150

[8] A. Szendrei, “Torsion theories in affine categories”, Acta Math. Acad. Sci. Hungar., 30 (1977), 351–369 | DOI | MR

[9] B. Csácány, “Varieties of affine modules”, Acta Sci. Math. (Szeged), 37 (1975), 3–10 | MR

[10] D. W. Blackett, “The near-ring of affine transformations”, Proc. Amer. Math. Soc., 7 (1956), 517–519 | DOI | MR | Zbl

[11] H. Gonshor, “On abstract affine near-rings”, Pacific J. Math., 14 (1964), 1237–1240 | DOI | MR | Zbl

[12] A. I. Kostrikin, Yu. I. Manin, Lineinaya algebra i geometriya, Nauka, M., 1986 | MR | Zbl

[13] G. Pilz, Near-Rings. The Theory and its Applications, North-Holland, Amsterdam, 1983 | MR | Zbl

[14] F. Borceux, Handbook of Categorical Algebra. I. Basic Category Theory, Cambridge Univ. Press, Cambridge, 1994 | MR

[15] S. Mac Lane, Categories for the Working Mathematician, Springer, New York, 1998 | MR | Zbl

[16] F. W. Anderson, K. R. Fuller, Rings and Categories of Modules, Springer, New York, 1974 | MR | Zbl

[17] P. A. Krylov, A. A. Tuganbaev, “Moduli nad koltsami formalnykh matrits”, Fundament. i prikl. matem., 15:8 (2009), 145–211 | MR