Special noncancellative commutative semigroup operations on the real numbers and distribution
Let R be the space of real numbers with the ordinary topology. Define x ⋆ 1 y = | x y | ( x , y ∈ R ) and x ⋆ 2 y = max { 1 , x } + max { 1 , y } ( x , y ∈ R ) . We show that there is no cancellative continuous semigroup operation which is distributed by ⋆ i ( i = 1 , 2 ) . Conversely we show that t...
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| Veröffentlicht in: | Acta mathematica Hungarica 2022-12, Vol.168 (2), p.363-372 |
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| container_title | Acta mathematica Hungarica |
| container_volume | 168 |
| creator | Miura, T. Niwa, N. Oka, H. Takahasi, S.-E. |
| description | Let
R
be the space of real numbers with the ordinary topology. Define
x
⋆
1
y
=
|
x
y
|
(
x
,
y
∈
R
)
and
x
⋆
2
y
=
max
{
1
,
x
}
+
max
{
1
,
y
}
(
x
,
y
∈
R
)
. We show that there is no cancellative continuous semigroup operation which is distributed by
⋆
i
(
i
=
1
,
2
)
. Conversely we show that there is no cancellative continuous semigroup operation which is distributive over
⋆
i
(
i
=
1
,
2
)
. Moreover we discuss the above arguments for a null semigroup operation on
R
. |
| doi_str_mv | 10.1007/s10474-022-01285-4 |
| format | Article |
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R
be the space of real numbers with the ordinary topology. Define
x
⋆
1
y
=
|
x
y
|
(
x
,
y
∈
R
)
and
x
⋆
2
y
=
max
{
1
,
x
}
+
max
{
1
,
y
}
(
x
,
y
∈
R
)
. We show that there is no cancellative continuous semigroup operation which is distributed by
⋆
i
(
i
=
1
,
2
)
. Conversely we show that there is no cancellative continuous semigroup operation which is distributive over
⋆
i
(
i
=
1
,
2
)
. Moreover we discuss the above arguments for a null semigroup operation on
R
.</description><identifier>ISSN: 0236-5294</identifier><identifier>EISSN: 1588-2632</identifier><identifier>DOI: 10.1007/s10474-022-01285-4</identifier><language>eng</language><publisher>Cham: Springer International Publishing</publisher><subject>Mathematics ; Mathematics and Statistics ; Real numbers ; Semigroups ; Topology</subject><ispartof>Acta mathematica Hungarica, 2022-12, Vol.168 (2), p.363-372</ispartof><rights>Akadémiai Kiadó, Budapest, Hungary 2022. 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-c200t-60046bb7775d3a3dd370aa503079de409a08d074dc395fdc21ee887834b031b33</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/s10474-022-01285-4$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s10474-022-01285-4$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27903,27904,41467,42536,51297</link.rule.ids></links><search><creatorcontrib>Miura, T.</creatorcontrib><creatorcontrib>Niwa, N.</creatorcontrib><creatorcontrib>Oka, H.</creatorcontrib><creatorcontrib>Takahasi, S.-E.</creatorcontrib><title>Special noncancellative commutative semigroup operations on the real numbers and distribution</title><title>Acta mathematica Hungarica</title><addtitle>Acta Math. Hungar</addtitle><description>Let
R
be the space of real numbers with the ordinary topology. Define
x
⋆
1
y
=
|
x
y
|
(
x
,
y
∈
R
)
and
x
⋆
2
y
=
max
{
1
,
x
}
+
max
{
1
,
y
}
(
x
,
y
∈
R
)
. We show that there is no cancellative continuous semigroup operation which is distributed by
⋆
i
(
i
=
1
,
2
)
. Conversely we show that there is no cancellative continuous semigroup operation which is distributive over
⋆
i
(
i
=
1
,
2
)
. Moreover we discuss the above arguments for a null semigroup operation on
R
.</description><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Real numbers</subject><subject>Semigroups</subject><subject>Topology</subject><issn>0236-5294</issn><issn>1588-2632</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2022</creationdate><recordtype>article</recordtype><recordid>eNp9kE1LxDAQhoMouK7-AU8Bz9HJV9MeZVFXWPCgHiWkSXbt0iY1aQX_vV0rePM0w_C878CD0CWFawqgbjIFoQQBxghQVkoijtCCyrIkrODsGC2A8YJIVolTdJbzHgAkB7FAb8-9t41pcYjBmmB925qh-fTYxq4bh3nPvmt2KY49jr1P0y2GjGPAw7vHyR_CY1f7lLEJDrsmD6mpxwN1jk62ps3-4ncu0ev93ctqTTZPD4-r2w2xDGAgBYAo6lopJR033DmuwBgJHFTlvIDKQOlACWd5JbfOMup9WaqSixo4rTlfoqu5t0_xY_R50Ps4pjC91EzJSlEpZTFRbKZsijknv9V9ajqTvjQFfdCoZ4160qh_NGoxhfgcyhMcdj79Vf-T-gYPp3Ze</recordid><startdate>20221201</startdate><enddate>20221201</enddate><creator>Miura, T.</creator><creator>Niwa, N.</creator><creator>Oka, H.</creator><creator>Takahasi, S.-E.</creator><general>Springer International Publishing</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20221201</creationdate><title>Special noncancellative commutative semigroup operations on the real numbers and distribution</title><author>Miura, T. ; Niwa, N. ; Oka, H. ; Takahasi, S.-E.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c200t-60046bb7775d3a3dd370aa503079de409a08d074dc395fdc21ee887834b031b33</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2022</creationdate><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Real numbers</topic><topic>Semigroups</topic><topic>Topology</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Miura, T.</creatorcontrib><creatorcontrib>Niwa, N.</creatorcontrib><creatorcontrib>Oka, H.</creatorcontrib><creatorcontrib>Takahasi, S.-E.</creatorcontrib><collection>CrossRef</collection><jtitle>Acta mathematica Hungarica</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Miura, T.</au><au>Niwa, N.</au><au>Oka, H.</au><au>Takahasi, S.-E.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Special noncancellative commutative semigroup operations on the real numbers and distribution</atitle><jtitle>Acta mathematica Hungarica</jtitle><stitle>Acta Math. Hungar</stitle><date>2022-12-01</date><risdate>2022</risdate><volume>168</volume><issue>2</issue><spage>363</spage><epage>372</epage><pages>363-372</pages><issn>0236-5294</issn><eissn>1588-2632</eissn><abstract>Let
R
be the space of real numbers with the ordinary topology. Define
x
⋆
1
y
=
|
x
y
|
(
x
,
y
∈
R
)
and
x
⋆
2
y
=
max
{
1
,
x
}
+
max
{
1
,
y
}
(
x
,
y
∈
R
)
. We show that there is no cancellative continuous semigroup operation which is distributed by
⋆
i
(
i
=
1
,
2
)
. Conversely we show that there is no cancellative continuous semigroup operation which is distributive over
⋆
i
(
i
=
1
,
2
)
. Moreover we discuss the above arguments for a null semigroup operation on
R
.</abstract><cop>Cham</cop><pub>Springer International Publishing</pub><doi>10.1007/s10474-022-01285-4</doi><tpages>10</tpages></addata></record> |
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| identifier | ISSN: 0236-5294 |
| ispartof | Acta mathematica Hungarica, 2022-12, Vol.168 (2), p.363-372 |
| issn | 0236-5294 1588-2632 |
| language | eng |
| recordid | cdi_proquest_journals_2759715556 |
| source | SpringerLink Journals - AutoHoldings |
| subjects | Mathematics Mathematics and Statistics Real numbers Semigroups Topology |
| title | Special noncancellative commutative semigroup operations on the real numbers and distribution |
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