Geodesic
Quasi-multiplicative maps on Baer semigroups
Glasgow mathematical journal, Tome 13 (1972) no. 2, pp. 107-110

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

A Baer semigroup is a semigroup 5 with 0 and 1 in which, for each x∈S, the left annihilator L(x) = {y∈S: yx = 0} of x is a principal left ideal generated by an idempotent and the right annihilator R(x) = {y∈S: xy = 0} of x is a principal right ideal generated by an idempotent. Baer semigroups are of interest because (see [5]) the left annihilators of the elements of a Baer semigroup S, L(S) = {L(x): x∈S}, form a bounded lattice and (see [4]) every bounded lattice arises in this manner. In this note we look at a type of map φ on a Baer semigroup S which has the property that Sφ is a Baer semigroup. (The homomorphic image of a Baer semigroup need not be a Baer semigroup. For a case where it is, see [7].) When the Baer semigroup is specialized to a Boolean algebra, this type of map generalizes Halmos's notion of a quantifier. 
Jr, C. S. Johnson. Quasi-multiplicative maps on Baer semigroups. Glasgow mathematical journal, Tome 13 (1972) no. 2, pp. 107-110. doi: 10.1017/S001708950000149X
@article{10_1017_S001708950000149X,
     author = {Jr, C. S. Johnson},
     title = {Quasi-multiplicative maps on {Baer} semigroups},
     journal = {Glasgow mathematical journal},
     pages = {107--110},
     year = {1972},
     volume = {13},
     number = {2},
     doi = {10.1017/S001708950000149X},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S001708950000149X/}
}
TY  - JOUR
AU  - Jr, C. S. Johnson
TI  - Quasi-multiplicative maps on Baer semigroups
JO  - Glasgow mathematical journal
PY  - 1972
SP  - 107
EP  - 110
VL  - 13
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.1017/S001708950000149X/
DO  - 10.1017/S001708950000149X
ID  - 10_1017_S001708950000149X
ER  - 
%0 Journal Article
%A Jr, C. S. Johnson
%T Quasi-multiplicative maps on Baer semigroups
%J Glasgow mathematical journal
%D 1972
%P 107-110
%V 13
%N 2
%U http://geodesic.mathdoc.fr/articles/10.1017/S001708950000149X/
%R 10.1017/S001708950000149X
%F 10_1017_S001708950000149X

[1] 1.Blyth, T. S. and Janowitz, M. F., On decreasing Baer semigroups, Bull. Soc. Roy. Sci. Liège 38 (1969), 414–423. Google Scholar

[2] 2.Foulis, D. J., Baer *-semigroups, Proc. Amer. Math. Soc. 11 (1960), 648–654. Google Scholar

[3] 3.Halmos, P. R., Algebraic logic I, monadic Boolean algebras, Compositio Math. 12 (1955), 217–249. Google Scholar

[4] 4.Janowitz, M. F., A semigroup approach to lattices, Canad. J. Math. 18 (1966), 1212–1223. Google Scholar | DOI

[5] 5.Janowitz, M. F., Baer semigroups, Duke Math. J. 32 (1965), 85–95. Google Scholar | DOI

[6] 6.Janowitz, M. F., Quantifiers and orthomodular lattices, Pacific J. Math. 13 (1963), 1241–1249. Google Scholar | DOI

[7] 7.Thorne, B. J., A–P congruences on Baer semigroups, Pacific J. Math. 28 (1969), 681–698. Google Scholar | DOI

Cité par Sources :