| Title:
|
Goldie extending elements in modular lattices (English) |
| Author:
|
Nimbhorkar, Shriram K. |
| Author:
|
Shroff, Rupal C. |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
142 |
| Issue:
|
2 |
| Year:
|
2017 |
| Pages:
|
163-180 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
modular lattice |
| Keyword:
|
Goldie extending element |
| MSC:
|
06B10 |
| MSC:
|
06C05 |
| idZBL:
|
Zbl 06738577 |
| idMR:
|
MR3660173 |
| DOI:
|
10.21136/MB.2016.0049-14 |
| . |
| Date available:
|
2017-05-23T09:59:22Z |
| Last updated:
|
2020-07-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/146750 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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