On radical classes of hemirings
Based on the concept of accessible subhemirings and inspired by the work on the general Kurosh-Amitsur radical theory for rings, this paper studies the lower radical classes and the hereditary radical classes of hemirings. We characterize radical classes of hemirings, and con- struct a lower radical...
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| Veröffentlicht in: | Tbilisi Mathematical Journal 2014-12, Vol.7 (1) |
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| container_title | Tbilisi Mathematical Journal |
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| creator | Inassaridze, Hvedri Mai, Le Hoang Tuyen, Nguyen Xuan |
| description | Based on the concept of accessible subhemirings and inspired by the work on the general
Kurosh-Amitsur radical theory for rings, this paper studies the lower radical classes and the
hereditary radical classes of hemirings. We characterize radical classes of hemirings, and con-
struct a lower radical class from a homomorphically closed class. We provide a necessary and
sufficient condition under which an upper radical class of hemirings becomes hereditary and
prove that an upper radical class of a regular class of semirings is hereditary. Besides, we show
that the Brown-McCoy radical class and a Jacobson-type radical class are hereditary. |
| doi_str_mv | 10.2478/tmj-2014-0007 |
| format | Article |
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Kurosh-Amitsur radical theory for rings, this paper studies the lower radical classes and the
hereditary radical classes of hemirings. We characterize radical classes of hemirings, and con-
struct a lower radical class from a homomorphically closed class. We provide a necessary and
sufficient condition under which an upper radical class of hemirings becomes hereditary and
prove that an upper radical class of a regular class of semirings is hereditary. Besides, we show
that the Brown-McCoy radical class and a Jacobson-type radical class are hereditary.</description><identifier>ISSN: 1875-158X</identifier><identifier>EISSN: 1512-0139</identifier><identifier>DOI: 10.2478/tmj-2014-0007</identifier><language>eng</language><publisher>De Gruyter Open</publisher><subject>06A99 ; 06F99 ; 16Y60 ; 18G05 ; 18G99 ; 8A30 ; accessible subhemiring ; hereditary radical class of hemiring ; lower radical class ; radical class of hemirings ; upper radical class</subject><ispartof>Tbilisi Mathematical Journal, 2014-12, Vol.7 (1)</ispartof><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c254t-4492031c40274de0b00bca99d571d2d8302966adb3d615cada4933a80d1bcb4c3</citedby><cites>FETCH-LOGICAL-c254t-4492031c40274de0b00bca99d571d2d8302966adb3d615cada4933a80d1bcb4c3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,27924,27925</link.rule.ids></links><search><creatorcontrib>Inassaridze, Hvedri</creatorcontrib><creatorcontrib>Mai, Le Hoang</creatorcontrib><creatorcontrib>Tuyen, Nguyen Xuan</creatorcontrib><title>On radical classes of hemirings</title><title>Tbilisi Mathematical Journal</title><description>Based on the concept of accessible subhemirings and inspired by the work on the general
Kurosh-Amitsur radical theory for rings, this paper studies the lower radical classes and the
hereditary radical classes of hemirings. We characterize radical classes of hemirings, and con-
struct a lower radical class from a homomorphically closed class. We provide a necessary and
sufficient condition under which an upper radical class of hemirings becomes hereditary and
prove that an upper radical class of a regular class of semirings is hereditary. Besides, we show
that the Brown-McCoy radical class and a Jacobson-type radical class are hereditary.</description><subject>06A99</subject><subject>06F99</subject><subject>16Y60</subject><subject>18G05</subject><subject>18G99</subject><subject>8A30</subject><subject>accessible subhemiring</subject><subject>hereditary radical class of hemiring</subject><subject>lower radical class</subject><subject>radical class of hemirings</subject><subject>upper radical class</subject><issn>1875-158X</issn><issn>1512-0139</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2014</creationdate><recordtype>article</recordtype><recordid>eNptj0tLxDAUhYMoOIyzdG3_QPTePJpmKYMvGJiNgruQJunY0ockHWT-vSnj0tU5i-9ezkfILcI9E6p6mIeOMkBBAUBdkBVKZBSQ68vcKyUpyurzmmxS6jKBQosSYEXu9mMRrW-d7QvX25RCKqam-ApDG9vxkG7IVWP7FDZ_uSYfz0_v21e627-8bR931DEpZiqEZsDRCWBK-AA1QO2s1l4q9MxXHJguS-tr7kuUznorNOe2Ao-1q4Xja0LPf12cUoqhMd-xHWw8GQSzCJosaBZBswhmXp35H9vPIfpwiMdTLqabjnHMS_-_U8h_AS5AVJw</recordid><startdate>20141201</startdate><enddate>20141201</enddate><creator>Inassaridze, Hvedri</creator><creator>Mai, Le Hoang</creator><creator>Tuyen, Nguyen Xuan</creator><general>De Gruyter Open</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20141201</creationdate><title>On radical classes of hemirings</title><author>Inassaridze, Hvedri ; Mai, Le Hoang ; Tuyen, Nguyen Xuan</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c254t-4492031c40274de0b00bca99d571d2d8302966adb3d615cada4933a80d1bcb4c3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2014</creationdate><topic>06A99</topic><topic>06F99</topic><topic>16Y60</topic><topic>18G05</topic><topic>18G99</topic><topic>8A30</topic><topic>accessible subhemiring</topic><topic>hereditary radical class of hemiring</topic><topic>lower radical class</topic><topic>radical class of hemirings</topic><topic>upper radical class</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Inassaridze, Hvedri</creatorcontrib><creatorcontrib>Mai, Le Hoang</creatorcontrib><creatorcontrib>Tuyen, Nguyen Xuan</creatorcontrib><collection>CrossRef</collection><jtitle>Tbilisi Mathematical Journal</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Inassaridze, Hvedri</au><au>Mai, Le Hoang</au><au>Tuyen, Nguyen Xuan</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>On radical classes of hemirings</atitle><jtitle>Tbilisi Mathematical Journal</jtitle><date>2014-12-01</date><risdate>2014</risdate><volume>7</volume><issue>1</issue><issn>1875-158X</issn><eissn>1512-0139</eissn><abstract>Based on the concept of accessible subhemirings and inspired by the work on the general
Kurosh-Amitsur radical theory for rings, this paper studies the lower radical classes and the
hereditary radical classes of hemirings. We characterize radical classes of hemirings, and con-
struct a lower radical class from a homomorphically closed class. We provide a necessary and
sufficient condition under which an upper radical class of hemirings becomes hereditary and
prove that an upper radical class of a regular class of semirings is hereditary. Besides, we show
that the Brown-McCoy radical class and a Jacobson-type radical class are hereditary.</abstract><pub>De Gruyter Open</pub><doi>10.2478/tmj-2014-0007</doi><tpages>6</tpages><oa>free_for_read</oa></addata></record> |
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| ispartof | Tbilisi Mathematical Journal, 2014-12, Vol.7 (1) |
| issn | 1875-158X 1512-0139 |
| language | eng |
| recordid | cdi_crossref_primary_10_2478_tmj_2014_0007 |
| source | Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals |
| subjects | 06A99 06F99 16Y60 18G05 18G99 8A30 accessible subhemiring hereditary radical class of hemiring lower radical class radical class of hemirings upper radical class |
| title | On radical classes of hemirings |
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