Loading…
Trinil clean index of a ring
From the concepts of clean index of rings, nil clean index of rings, and weakly nil clean index of rings, we expand them by introducing the new concept, that is, trinil clean index of a ring. From any element a of a ring R with unity, we set τ( a ): ={ e ∈ R | e 3 = e and a − e ∈ Nil ( R )}, where N...
Saved in:
| Published in: | Journal of physics. Conference series 2021-05, Vol.1872 (1), p.12016 |
|---|---|
| Main Authors: | , , , , |
| Format: | Article |
| Language: | English |
| Subjects: | |
| Citations: | Items that this one cites |
| Online Access: | Get full text |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| cited_by | |
|---|---|
| cites | cdi_FETCH-LOGICAL-c2396-6bf2fed96daf67ae232edd5722732eb81830befc4d52cf0259d90a4848f64cf53 |
| container_end_page | |
| container_issue | 1 |
| container_start_page | 12016 |
| container_title | Journal of physics. Conference series |
| container_volume | 1872 |
| creator | Mu’in, A Irawati, S Susanto, H Agung, M Marubayashi, H |
| description | From the concepts of clean index of rings, nil clean index of rings, and weakly nil clean index of rings, we expand them by introducing the new concept, that is, trinil clean index of a ring. From any element
a
of a ring
R
with unity, we set τ(
a
): ={
e
∈
R
|
e
3
=
e
and
a
−
e
∈
Nil
(
R
)}, where Nil(
R
) is the set of all nilpotent elements of
R
; trinil clean index of
R
is defined by sup{|τ(
a
)||
a
∈
R
} and it is denoted by
Trinin(R)
. In this article, it will be investigated some properties of trinil clean index of any ring, ring homomorphism, and direct product. Some applications of determining trinil clean index of integral domains are also provided. We also determined the trinil clean index of ℤ
n
. |
| doi_str_mv | 10.1088/1742-6596/1872/1/012016 |
| format | article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_2528496622</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2528496622</sourcerecordid><originalsourceid>FETCH-LOGICAL-c2396-6bf2fed96daf67ae232edd5722732eb81830befc4d52cf0259d90a4848f64cf53</originalsourceid><addsrcrecordid>eNqFUE1LxDAQDaLguvoPBAuea5PJ91EWXYUFL-s5pPmQLrVdExf035tSWY_OZYaZ997wHkI3BN8RrFRDJINacC0aoiQ0pMEEMBEnaHG8nB5npc7RRc47jGkpuUDX29QNXV-5Ptih6gYfvqoxVrYq67dLdBZtn8PVb1-i18eH7eqp3rysn1f3m9oB1aIWbYQYvBbeRiFtAArBey4BZJlaRRTFbYiOeQ4uYuDaa2yZYioK5iKnS3Q76-7T-HEI-dPsxkMayksDHBTTQgAUlJxRLo05pxDNPnXvNn0bgs0UhZlMmsmwmaIwxMxRFCadmd24_5P-j_UD_FZd-A</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2528496622</pqid></control><display><type>article</type><title>Trinil clean index of a ring</title><source>Full-Text Journals in Chemistry (Open access)</source><source>Publicly Available Content (ProQuest)</source><creator>Mu’in, A ; Irawati, S ; Susanto, H ; Agung, M ; Marubayashi, H</creator><creatorcontrib>Mu’in, A ; Irawati, S ; Susanto, H ; Agung, M ; Marubayashi, H</creatorcontrib><description>From the concepts of clean index of rings, nil clean index of rings, and weakly nil clean index of rings, we expand them by introducing the new concept, that is, trinil clean index of a ring. From any element
a
of a ring
R
with unity, we set τ(
a
): ={
e
∈
R
|
e
3
=
e
and
a
−
e
∈
Nil
(
R
)}, where Nil(
R
) is the set of all nilpotent elements of
R
; trinil clean index of
R
is defined by sup{|τ(
a
)||
a
∈
R
} and it is denoted by
Trinin(R)
. In this article, it will be investigated some properties of trinil clean index of any ring, ring homomorphism, and direct product. Some applications of determining trinil clean index of integral domains are also provided. We also determined the trinil clean index of ℤ
n
.</description><identifier>ISSN: 1742-6588</identifier><identifier>EISSN: 1742-6596</identifier><identifier>DOI: 10.1088/1742-6596/1872/1/012016</identifier><language>eng</language><publisher>Bristol: IOP Publishing</publisher><subject>Homomorphisms ; Physics</subject><ispartof>Journal of physics. Conference series, 2021-05, Vol.1872 (1), p.12016</ispartof><rights>Published under licence by IOP Publishing Ltd</rights><rights>2021. This work is published under http://creativecommons.org/licenses/by/3.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c2396-6bf2fed96daf67ae232edd5722732eb81830befc4d52cf0259d90a4848f64cf53</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://www.proquest.com/docview/2528496622?pq-origsite=primo$$EHTML$$P50$$Gproquest$$Hfree_for_read</linktohtml><link.rule.ids>314,780,784,25752,27923,27924,37011,44589</link.rule.ids></links><search><creatorcontrib>Mu’in, A</creatorcontrib><creatorcontrib>Irawati, S</creatorcontrib><creatorcontrib>Susanto, H</creatorcontrib><creatorcontrib>Agung, M</creatorcontrib><creatorcontrib>Marubayashi, H</creatorcontrib><title>Trinil clean index of a ring</title><title>Journal of physics. Conference series</title><addtitle>J. Phys.: Conf. Ser</addtitle><description>From the concepts of clean index of rings, nil clean index of rings, and weakly nil clean index of rings, we expand them by introducing the new concept, that is, trinil clean index of a ring. From any element
a
of a ring
R
with unity, we set τ(
a
): ={
e
∈
R
|
e
3
=
e
and
a
−
e
∈
Nil
(
R
)}, where Nil(
R
) is the set of all nilpotent elements of
R
; trinil clean index of
R
is defined by sup{|τ(
a
)||
a
∈
R
} and it is denoted by
Trinin(R)
. In this article, it will be investigated some properties of trinil clean index of any ring, ring homomorphism, and direct product. Some applications of determining trinil clean index of integral domains are also provided. We also determined the trinil clean index of ℤ
n
.</description><subject>Homomorphisms</subject><subject>Physics</subject><issn>1742-6588</issn><issn>1742-6596</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2021</creationdate><recordtype>article</recordtype><sourceid>PIMPY</sourceid><recordid>eNqFUE1LxDAQDaLguvoPBAuea5PJ91EWXYUFL-s5pPmQLrVdExf035tSWY_OZYaZ997wHkI3BN8RrFRDJINacC0aoiQ0pMEEMBEnaHG8nB5npc7RRc47jGkpuUDX29QNXV-5Ptih6gYfvqoxVrYq67dLdBZtn8PVb1-i18eH7eqp3rysn1f3m9oB1aIWbYQYvBbeRiFtAArBey4BZJlaRRTFbYiOeQ4uYuDaa2yZYioK5iKnS3Q76-7T-HEI-dPsxkMayksDHBTTQgAUlJxRLo05pxDNPnXvNn0bgs0UhZlMmsmwmaIwxMxRFCadmd24_5P-j_UD_FZd-A</recordid><startdate>20210501</startdate><enddate>20210501</enddate><creator>Mu’in, A</creator><creator>Irawati, S</creator><creator>Susanto, H</creator><creator>Agung, M</creator><creator>Marubayashi, H</creator><general>IOP Publishing</general><scope>O3W</scope><scope>TSCCA</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>8FD</scope><scope>8FE</scope><scope>8FG</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>ARAPS</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>H8D</scope><scope>HCIFZ</scope><scope>L7M</scope><scope>P5Z</scope><scope>P62</scope><scope>PIMPY</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope></search><sort><creationdate>20210501</creationdate><title>Trinil clean index of a ring</title><author>Mu’in, A ; Irawati, S ; Susanto, H ; Agung, M ; Marubayashi, H</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c2396-6bf2fed96daf67ae232edd5722732eb81830befc4d52cf0259d90a4848f64cf53</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2021</creationdate><topic>Homomorphisms</topic><topic>Physics</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Mu’in, A</creatorcontrib><creatorcontrib>Irawati, S</creatorcontrib><creatorcontrib>Susanto, H</creatorcontrib><creatorcontrib>Agung, M</creatorcontrib><creatorcontrib>Marubayashi, H</creatorcontrib><collection>IOP_英国物理学会OA刊</collection><collection>IOPscience (Open Access)</collection><collection>CrossRef</collection><collection>Technology Research Database</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>ProQuest Central (Alumni)</collection><collection>ProQuest Central</collection><collection>Advanced Technologies & Aerospace Collection</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central</collection><collection>Aerospace Database</collection><collection>SciTech Premium Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Advanced Technologies & Aerospace Database</collection><collection>ProQuest Advanced Technologies & Aerospace Collection</collection><collection>Publicly Available Content (ProQuest)</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest Central China</collection><jtitle>Journal of physics. Conference series</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Mu’in, A</au><au>Irawati, S</au><au>Susanto, H</au><au>Agung, M</au><au>Marubayashi, H</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Trinil clean index of a ring</atitle><jtitle>Journal of physics. Conference series</jtitle><addtitle>J. Phys.: Conf. Ser</addtitle><date>2021-05-01</date><risdate>2021</risdate><volume>1872</volume><issue>1</issue><spage>12016</spage><pages>12016-</pages><issn>1742-6588</issn><eissn>1742-6596</eissn><abstract>From the concepts of clean index of rings, nil clean index of rings, and weakly nil clean index of rings, we expand them by introducing the new concept, that is, trinil clean index of a ring. From any element
a
of a ring
R
with unity, we set τ(
a
): ={
e
∈
R
|
e
3
=
e
and
a
−
e
∈
Nil
(
R
)}, where Nil(
R
) is the set of all nilpotent elements of
R
; trinil clean index of
R
is defined by sup{|τ(
a
)||
a
∈
R
} and it is denoted by
Trinin(R)
. In this article, it will be investigated some properties of trinil clean index of any ring, ring homomorphism, and direct product. Some applications of determining trinil clean index of integral domains are also provided. We also determined the trinil clean index of ℤ
n
.</abstract><cop>Bristol</cop><pub>IOP Publishing</pub><doi>10.1088/1742-6596/1872/1/012016</doi><tpages>7</tpages><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 1742-6588 |
| ispartof | Journal of physics. Conference series, 2021-05, Vol.1872 (1), p.12016 |
| issn | 1742-6588 1742-6596 |
| language | eng |
| recordid | cdi_proquest_journals_2528496622 |
| source | Full-Text Journals in Chemistry (Open access); Publicly Available Content (ProQuest) |
| subjects | Homomorphisms Physics |
| title | Trinil clean index of a ring |
| url | http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-13T03%3A01%3A33IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Trinil%20clean%20index%20of%20a%20ring&rft.jtitle=Journal%20of%20physics.%20Conference%20series&rft.au=Mu%E2%80%99in,%20A&rft.date=2021-05-01&rft.volume=1872&rft.issue=1&rft.spage=12016&rft.pages=12016-&rft.issn=1742-6588&rft.eissn=1742-6596&rft_id=info:doi/10.1088/1742-6596/1872/1/012016&rft_dat=%3Cproquest_cross%3E2528496622%3C/proquest_cross%3E%3Cgrp_id%3Ecdi_FETCH-LOGICAL-c2396-6bf2fed96daf67ae232edd5722732eb81830befc4d52cf0259d90a4848f64cf53%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_pqid=2528496622&rft_id=info:pmid/&rfr_iscdi=true |