Congruence-simple multiplicatively idempotent semirings
Let S be a multiplicatively idempotent congruence-simple semiring. We show that | S | = 2 if S has a multiplicatively absorbing element. We also prove that if S is finite then either | S | = 2 or S ≅ End ( L ) or S op ≅ End ( L ) where L is the 2-element semilattice. It seems to be an open question,...
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| Veröffentlicht in: | Algebra universalis 2023-05, Vol.84 (2), Article 13 |
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| container_issue | 2 |
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| container_title | Algebra universalis |
| container_volume | 84 |
| creator | Kepka, Tomáš Korbelář, Miroslav Landsmann, Günter |
| description | Let
S
be a multiplicatively idempotent congruence-simple semiring. We show that
|
S
|
=
2
if
S
has a multiplicatively absorbing element. We also prove that if
S
is finite then either
|
S
|
=
2
or
S
≅
End
(
L
)
or
S
op
≅
End
(
L
)
where
L
is the 2-element semilattice. It seems to be an open question, whether
S
can be infinite at all. |
| doi_str_mv | 10.1007/s00012-023-00807-7 |
| format | Article |
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S
be a multiplicatively idempotent congruence-simple semiring. We show that
|
S
|
=
2
if
S
has a multiplicatively absorbing element. We also prove that if
S
is finite then either
|
S
|
=
2
or
S
≅
End
(
L
)
or
S
op
≅
End
(
L
)
where
L
is the 2-element semilattice. It seems to be an open question, whether
S
can be infinite at all.</description><identifier>ISSN: 0002-5240</identifier><identifier>EISSN: 1420-8911</identifier><identifier>DOI: 10.1007/s00012-023-00807-7</identifier><language>eng</language><publisher>Cham: Springer International Publishing</publisher><subject>Algebra ; Mathematics ; Mathematics and Statistics ; Rings (mathematics)</subject><ispartof>Algebra universalis, 2023-05, Vol.84 (2), Article 13</ispartof><rights>The Author(s), under exclusive licence to Springer Nature Switzerland AG 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c270t-7fff977c400875571dc17594a24ce859785ecfd1e8b8398299c9a04c500bc3813</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s00012-023-00807-7$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s00012-023-00807-7$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27901,27902,41464,42533,51294</link.rule.ids></links><search><creatorcontrib>Kepka, Tomáš</creatorcontrib><creatorcontrib>Korbelář, Miroslav</creatorcontrib><creatorcontrib>Landsmann, Günter</creatorcontrib><title>Congruence-simple multiplicatively idempotent semirings</title><title>Algebra universalis</title><addtitle>Algebra Univers</addtitle><description>Let
S
be a multiplicatively idempotent congruence-simple semiring. We show that
|
S
|
=
2
if
S
has a multiplicatively absorbing element. We also prove that if
S
is finite then either
|
S
|
=
2
or
S
≅
End
(
L
)
or
S
op
≅
End
(
L
)
where
L
is the 2-element semilattice. It seems to be an open question, whether
S
can be infinite at all.</description><subject>Algebra</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Rings (mathematics)</subject><issn>0002-5240</issn><issn>1420-8911</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><recordid>eNp9kE1LxDAQhoMoWFf_gKeC5-gkbZzkKMUvWPCi59BNp0uWfpm0wv57Wyt4cy5zmPd9Z-Zh7FrArQDAuwgAQnKQGQfQgBxPWCJyCVwbIU5ZMs8lVzKHc3YR42FRo1EJw6Lv9mGizhGPvh0aStupGf3QeFeO_ouaY-oraod-pG5MI7U--G4fL9lZXTaRrn77hn08Pb4XL3z79vxaPGy5kwgjx7quDaLL56tQKRSVE6hMXsrckVYGtSJXV4L0TmdGS2OcKSF3CmDnMi2yDbtZc4fQf04UR3vop9DNK61Efa_mEjir5KpyoY8xUG2H4NsyHK0AuwCyKyA7A7I_gOxiylZTHJaXKPxF_-P6BgL2Z_8</recordid><startdate>20230501</startdate><enddate>20230501</enddate><creator>Kepka, Tomáš</creator><creator>Korbelář, Miroslav</creator><creator>Landsmann, Günter</creator><general>Springer International Publishing</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20230501</creationdate><title>Congruence-simple multiplicatively idempotent semirings</title><author>Kepka, Tomáš ; Korbelář, Miroslav ; Landsmann, Günter</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c270t-7fff977c400875571dc17594a24ce859785ecfd1e8b8398299c9a04c500bc3813</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>Algebra</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Rings (mathematics)</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Kepka, Tomáš</creatorcontrib><creatorcontrib>Korbelář, Miroslav</creatorcontrib><creatorcontrib>Landsmann, Günter</creatorcontrib><collection>CrossRef</collection><jtitle>Algebra universalis</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Kepka, Tomáš</au><au>Korbelář, Miroslav</au><au>Landsmann, Günter</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Congruence-simple multiplicatively idempotent semirings</atitle><jtitle>Algebra universalis</jtitle><stitle>Algebra Univers</stitle><date>2023-05-01</date><risdate>2023</risdate><volume>84</volume><issue>2</issue><artnum>13</artnum><issn>0002-5240</issn><eissn>1420-8911</eissn><abstract>Let
S
be a multiplicatively idempotent congruence-simple semiring. We show that
|
S
|
=
2
if
S
has a multiplicatively absorbing element. We also prove that if
S
is finite then either
|
S
|
=
2
or
S
≅
End
(
L
)
or
S
op
≅
End
(
L
)
where
L
is the 2-element semilattice. It seems to be an open question, whether
S
can be infinite at all.</abstract><cop>Cham</cop><pub>Springer International Publishing</pub><doi>10.1007/s00012-023-00807-7</doi></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0002-5240 |
| ispartof | Algebra universalis, 2023-05, Vol.84 (2), Article 13 |
| issn | 0002-5240 1420-8911 |
| language | eng |
| recordid | cdi_proquest_journals_2786555517 |
| source | SpringerLink Journals |
| subjects | Algebra Mathematics Mathematics and Statistics Rings (mathematics) |
| title | Congruence-simple multiplicatively idempotent semirings |
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