Geodesic
Asymmetry in the lattice of kernel functors
Glasgow mathematical journal, Tome 33 (1991) no. 1, pp. 95-97

Voir la notice de l'article provenant de la source Cambridge University Press

Much of the research done by different authors on the lattice of kernel functors (equivalently, linear topologies) has been summarized by Golan in [2]. More recently, the rings whose lattices of kernel functors are linearly ordered were introduced in [3] as a categorical generalization of valuation rings in the non-commutative case. Results (and examples) in [3] show that there is an abundance of non-commutative rings R whose lattices (R), both in Mod-R and R-Mod, are simultaneously linearly ordered; however, the question of the symmetry of this condition remained open. Here we will prove that, for every natural number n≥3, there exists a ring Rn such that (Mod-Rn) is a linearly ordered lattice of n elements, whereas (Rn-Mod) is not linearly ordered. 
Viola-Prioli, Ana M. de; Viola-Prioli, Jorge E. Asymmetry in the lattice of kernel functors. Glasgow mathematical journal, Tome 33 (1991) no. 1, pp. 95-97. doi: 10.1017/S0017089500008089
@article{10_1017_S0017089500008089,
     author = {Viola-Prioli, Ana M. de and Viola-Prioli, Jorge E.},
     title = {Asymmetry in the lattice of kernel functors},
     journal = {Glasgow mathematical journal},
     pages = {95--97},
     year = {1991},
     volume = {33},
     number = {1},
     doi = {10.1017/S0017089500008089},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089500008089/}
}
TY  - JOUR
AU  - Viola-Prioli, Ana M. de
AU  - Viola-Prioli, Jorge E.
TI  - Asymmetry in the lattice of kernel functors
JO  - Glasgow mathematical journal
PY  - 1991
SP  - 95
EP  - 97
VL  - 33
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.1017/S0017089500008089/
DO  - 10.1017/S0017089500008089
ID  - 10_1017_S0017089500008089
ER  - 
%0 Journal Article
%A Viola-Prioli, Ana M. de
%A Viola-Prioli, Jorge E.
%T Asymmetry in the lattice of kernel functors
%J Glasgow mathematical journal
%D 1991
%P 95-97
%V 33
%N 1
%U http://geodesic.mathdoc.fr/articles/10.1017/S0017089500008089/
%R 10.1017/S0017089500008089
%F 10_1017_S0017089500008089

[1] 1.Cohn, P. M., Free rings and their relations (Academic Press, 1971). Google Scholar

[2] 2.Golan, J. S., Linear topologies on a ring: an overview, Research Notes in Mathematics No. 159 (Pitman, 1987). Google Scholar

[3] 3.de Viola-Prioli, A. M. and Viola-Prioli, J., Rings whose kernel functors are linearly ordered, Pacific J. Math. 132 (1988), 21–34. Google Scholar | DOI

Cité par Sources :