Geodesic
Goldie extending elements in modular lattices
Mathematica Bohemica, Tome 142 (2017) no. 2, pp. 163-180

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

The concept of a Goldie extending module is generalized to a Goldie extending element in a lattice. An element $a$ of a lattice $L$ with $0$ is said to be a Goldie extending element if and only if for every $b \leq a$ there exists a direct summand $c$ of $a$ such that $b \wedge c$ is essential in both $b$ and $c$. Some properties of such elements are obtained in the context of modular lattices. We give a necessary condition for the direct sum of Goldie extending elements to be Goldie extending. Some characterizations of a decomposition of a Goldie extending element in such a lattice are given. The concepts of an $a$-injective and an $a$-ejective element are introduced in a lattice and their properties related to extending elements are discussed.
DOI : 10.21136/MB.2016.0049-14
Classification : 06B10, 06C05
Keywords: modular lattice; Goldie extending element 
@article{10_21136_MB_2016_0049_14,
     author = {Nimbhorkar, Shriram K. and Shroff, Rupal C.},
     title = {Goldie extending elements in modular lattices},
     journal = {Mathematica Bohemica},
     pages = {163--180},
     publisher = {mathdoc},
     volume = {142},
     number = {2},
     year = {2017},
     doi = {10.21136/MB.2016.0049-14},
     mrnumber = {3660173},
     zbl = {06738577},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/MB.2016.0049-14/}
}
TY  - JOUR
AU  - Nimbhorkar, Shriram K.
AU  - Shroff, Rupal C.
TI  - Goldie extending elements in modular lattices
JO  - Mathematica Bohemica
PY  - 2017
SP  - 163
EP  - 180
VL  - 142
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.21136/MB.2016.0049-14/
DO  - 10.21136/MB.2016.0049-14
LA  - en
ID  - 10_21136_MB_2016_0049_14
ER  - 
%0 Journal Article
%A Nimbhorkar, Shriram K.
%A Shroff, Rupal C.
%T Goldie extending elements in modular lattices
%J Mathematica Bohemica
%D 2017
%P 163-180
%V 142
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.21136/MB.2016.0049-14/
%R 10.21136/MB.2016.0049-14
%G en
%F 10_21136_MB_2016_0049_14
Nimbhorkar, Shriram K.; Shroff, Rupal C. Goldie extending elements in modular lattices. Mathematica Bohemica, Tome 142 (2017) no. 2, pp. 163-180. doi: 10.21136/MB.2016.0049-14

Cité par Sources :