Geodesic
A Semigroup Approach to Lattices
Canadian journal of mathematics, Tome 18 (1966) no. 1, pp. 1212-1223

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

In (3, p. 85) we denned a Baer semigroup to be a multiplicative semigroup with 0 having the property that the left (right) annihilator of every element is a principal left (right) ideal generated by an idempotent. We showed (3, Lemma 1(vi) and Theorem 5, p. 86) that with set inclusion as the partial order, the set of left annihilators and the set of right annihilators of elements of a Baer semigroup form dual isomorphic lattices with 0 and 1. 
Janowitz, M. F. A Semigroup Approach to Lattices. Canadian journal of mathematics, Tome 18 (1966) no. 1, pp. 1212-1223. doi: 10.4153/CJM-1966-119-5
@article{10_4153_CJM_1966_119_5,
     author = {Janowitz, M. F.},
     title = {A {Semigroup} {Approach} to {Lattices}},
     journal = {Canadian journal of mathematics},
     pages = {1212--1223},
     year = {1966},
     volume = {18},
     number = {1},
     doi = {10.4153/CJM-1966-119-5},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1966-119-5/}
}
TY  - JOUR
AU  - Janowitz, M. F.
TI  - A Semigroup Approach to Lattices
JO  - Canadian journal of mathematics
PY  - 1966
SP  - 1212
EP  - 1223
VL  - 18
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1966-119-5/
DO  - 10.4153/CJM-1966-119-5
ID  - 10_4153_CJM_1966_119_5
ER  - 
%0 Journal Article
%A Janowitz, M. F.
%T A Semigroup Approach to Lattices
%J Canadian journal of mathematics
%D 1966
%P 1212-1223
%V 18
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1966-119-5/
%R 10.4153/CJM-1966-119-5
%F 10_4153_CJM_1966_119_5

[1] 1. Croisot, R., Applications residuées, Ann. Sci. Ecole Norm. Sup., 73 (1956), 453–474, Google Scholar

[2] 2. Foulis, D. J., Conditions for the modularity of an orthomodular lattice, Pacific J. Math., 11 (1961), 889–895. Google Scholar

[3] 3. Janowitz, M. F., Boer semigroups, Duke Math. J., 32 (1965), 85–95. Google Scholar

[4] 4. Janowitz, M. F., Quasi-orthomodular lattices, UNM Technical Report No. 42 (1963). Google Scholar

[5] 5. Maeda, F., Kontinuierliche Geometrien (Berlin, 1958). Google Scholar

Cité par Sources :