Direct summands of Goldie extending elements in modular lattices
In this paper some results on direct summands of Goldie extending elements are studied in a modular 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 essent...
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| Format: | Article |
| Language: | English |
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Institute of Mathematics of the Czech Academy of Science
2022-10-01
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| Series: | Mathematica Bohemica |
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| Online Access: | http://mb.math.cas.cz/full/147/3/mb147_3_6.pdf |
| _version_ | 1817986977681637376 |
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| author | Rupal Shroff |
| author_facet | Rupal Shroff |
| author_sort | Rupal Shroff |
| collection | DOAJ |
| description | In this paper some results on direct summands of Goldie extending elements are studied in a modular 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 characterizations of decomposition of a Goldie extending element in a modular lattice are obtained. |
| first_indexed | 2024-04-14T00:16:08Z |
| format | Article |
| id | doaj.art-6d72f9c82ccd4b269966f8aea0c8e3cc |
| institution | Directory Open Access Journal |
| issn | 0862-7959 2464-7136 |
| language | English |
| last_indexed | 2024-04-14T00:16:08Z |
| publishDate | 2022-10-01 |
| publisher | Institute of Mathematics of the Czech Academy of Science |
| record_format | Article |
| series | Mathematica Bohemica |
| spelling | doaj.art-6d72f9c82ccd4b269966f8aea0c8e3cc2022-12-22T02:23:07ZengInstitute of Mathematics of the Czech Academy of ScienceMathematica Bohemica0862-79592464-71362022-10-01147335936810.21136/MB.2021.0181-20MB.2021.0181-20Direct summands of Goldie extending elements in modular latticesRupal ShroffIn this paper some results on direct summands of Goldie extending elements are studied in a modular 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 characterizations of decomposition of a Goldie extending element in a modular lattice are obtained.http://mb.math.cas.cz/full/147/3/mb147_3_6.pdf modular lattice direct summand goldie extending element |
| spellingShingle | Rupal Shroff Direct summands of Goldie extending elements in modular lattices Mathematica Bohemica modular lattice direct summand goldie extending element |
| title | Direct summands of Goldie extending elements in modular lattices |
| title_full | Direct summands of Goldie extending elements in modular lattices |
| title_fullStr | Direct summands of Goldie extending elements in modular lattices |
| title_full_unstemmed | Direct summands of Goldie extending elements in modular lattices |
| title_short | Direct summands of Goldie extending elements in modular lattices |
| title_sort | direct summands of goldie extending elements in modular lattices |
| topic | modular lattice direct summand goldie extending element |
| url | http://mb.math.cas.cz/full/147/3/mb147_3_6.pdf |
| work_keys_str_mv | AT rupalshroff directsummandsofgoldieextendingelementsinmodularlattices |