The bands satisfying the strong isomorphism property
The power semigroup, or global, of a semigroup S is the set P ( S ) of all nonempty subsets of S equipped with the naturally defined multiplication. A class K of semigroups is globally determined if any two semigroups of K with isomorphic globals are themselves isomorphic. A class K of semigroups is...
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| Veröffentlicht in: | Semigroup forum 2019-04, Vol.98 (2), p.327-337 |
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| container_title | Semigroup forum |
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| creator | Yu, Baomin Zhao, Xianzhong |
| description | The power semigroup, or global, of a semigroup
S
is the set
P
(
S
) of all nonempty subsets of
S
equipped with the naturally defined multiplication. A class
K
of semigroups is globally determined if any two semigroups of
K
with isomorphic globals are themselves isomorphic. A class
K
of semigroups is said to satisfy the strong isomorphism property if for each pair
S
,
T
∈
K
and each isomorphism
ψ
from
P
(
S
) onto
P
(
T
),
ψ
(
S
¯
)
=
T
¯
, where
S
¯
=
{
{
s
}
∣
s
∈
S
}
⊆
P
(
S
)
,
T
¯
=
{
{
t
}
∣
t
∈
T
}
⊆
P
(
T
)
, and hence
S
≅
T
. In this paper we investigate classes of bands satisfying the strong isomorphism property. We provide a description of the largest subclass
K
¯
of
K
satisfying the strong isomorphism property for a globally determined class
K
of semigroups, and give some characterizations of the members of
B
¯
for class
B
of all bands. |
| doi_str_mv | 10.1007/s00233-019-09998-9 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_2186693385</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2186693385</sourcerecordid><originalsourceid>FETCH-LOGICAL-c270t-9f050f17c9fb5369fdec29317fc8543c209d1ade1b6fdf8adb23360a3dbec1123</originalsourceid><addsrcrecordid>eNp9kMtOwzAQRS0EEqXwA6wisTbMeJqHl6gCilSJTVlbTmy3qWgSPOmif48hSOxYzUP3ztUcIW4R7hGgfGAARSQBtQStdSX1mZjhgpRUSOW5mAFQKVGjuhRXzHtIMxQ0E4vNzme17RxnbMeWw6ntttmYljzGPrUt94c-DruWD9kQ-8HH8XQtLoL9YH_zW-fi_flps1zJ9dvL6_JxLRtVwih1gBwClo0OdU6FDs43ShOWoanyBTUKtEPrPNZFcKGyrk4_FGDJ1b5BVDQXd9PdFPx59DyafX-MXYo0Cqui0ERVnlRqUjWxZ44-mCG2BxtPBsF80zETHZPomB86RicTTSZO4m7r49_pf1xf5tVn8A</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2186693385</pqid></control><display><type>article</type><title>The bands satisfying the strong isomorphism property</title><source>Springer Nature - Complete Springer Journals</source><creator>Yu, Baomin ; Zhao, Xianzhong</creator><creatorcontrib>Yu, Baomin ; Zhao, Xianzhong</creatorcontrib><description>The power semigroup, or global, of a semigroup
S
is the set
P
(
S
) of all nonempty subsets of
S
equipped with the naturally defined multiplication. A class
K
of semigroups is globally determined if any two semigroups of
K
with isomorphic globals are themselves isomorphic. A class
K
of semigroups is said to satisfy the strong isomorphism property if for each pair
S
,
T
∈
K
and each isomorphism
ψ
from
P
(
S
) onto
P
(
T
),
ψ
(
S
¯
)
=
T
¯
, where
S
¯
=
{
{
s
}
∣
s
∈
S
}
⊆
P
(
S
)
,
T
¯
=
{
{
t
}
∣
t
∈
T
}
⊆
P
(
T
)
, and hence
S
≅
T
. In this paper we investigate classes of bands satisfying the strong isomorphism property. We provide a description of the largest subclass
K
¯
of
K
satisfying the strong isomorphism property for a globally determined class
K
of semigroups, and give some characterizations of the members of
B
¯
for class
B
of all bands.</description><identifier>ISSN: 0037-1912</identifier><identifier>EISSN: 1432-2137</identifier><identifier>DOI: 10.1007/s00233-019-09998-9</identifier><language>eng</language><publisher>New York: Springer US</publisher><subject>Algebra ; Isomorphism ; Mathematics ; Mathematics and Statistics ; Product development ; Research Article</subject><ispartof>Semigroup forum, 2019-04, Vol.98 (2), p.327-337</ispartof><rights>Springer Science+Business Media, LLC, part of Springer Nature 2019</rights><rights>Copyright Springer Nature B.V. 2019</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c270t-9f050f17c9fb5369fdec29317fc8543c209d1ade1b6fdf8adb23360a3dbec1123</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/s00233-019-09998-9$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s00233-019-09998-9$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27903,27904,41467,42536,51297</link.rule.ids></links><search><creatorcontrib>Yu, Baomin</creatorcontrib><creatorcontrib>Zhao, Xianzhong</creatorcontrib><title>The bands satisfying the strong isomorphism property</title><title>Semigroup forum</title><addtitle>Semigroup Forum</addtitle><description>The power semigroup, or global, of a semigroup
S
is the set
P
(
S
) of all nonempty subsets of
S
equipped with the naturally defined multiplication. A class
K
of semigroups is globally determined if any two semigroups of
K
with isomorphic globals are themselves isomorphic. A class
K
of semigroups is said to satisfy the strong isomorphism property if for each pair
S
,
T
∈
K
and each isomorphism
ψ
from
P
(
S
) onto
P
(
T
),
ψ
(
S
¯
)
=
T
¯
, where
S
¯
=
{
{
s
}
∣
s
∈
S
}
⊆
P
(
S
)
,
T
¯
=
{
{
t
}
∣
t
∈
T
}
⊆
P
(
T
)
, and hence
S
≅
T
. In this paper we investigate classes of bands satisfying the strong isomorphism property. We provide a description of the largest subclass
K
¯
of
K
satisfying the strong isomorphism property for a globally determined class
K
of semigroups, and give some characterizations of the members of
B
¯
for class
B
of all bands.</description><subject>Algebra</subject><subject>Isomorphism</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Product development</subject><subject>Research Article</subject><issn>0037-1912</issn><issn>1432-2137</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2019</creationdate><recordtype>article</recordtype><recordid>eNp9kMtOwzAQRS0EEqXwA6wisTbMeJqHl6gCilSJTVlbTmy3qWgSPOmif48hSOxYzUP3ztUcIW4R7hGgfGAARSQBtQStdSX1mZjhgpRUSOW5mAFQKVGjuhRXzHtIMxQ0E4vNzme17RxnbMeWw6ntttmYljzGPrUt94c-DruWD9kQ-8HH8XQtLoL9YH_zW-fi_flps1zJ9dvL6_JxLRtVwih1gBwClo0OdU6FDs43ShOWoanyBTUKtEPrPNZFcKGyrk4_FGDJ1b5BVDQXd9PdFPx59DyafX-MXYo0Cqui0ERVnlRqUjWxZ44-mCG2BxtPBsF80zETHZPomB86RicTTSZO4m7r49_pf1xf5tVn8A</recordid><startdate>20190415</startdate><enddate>20190415</enddate><creator>Yu, Baomin</creator><creator>Zhao, Xianzhong</creator><general>Springer US</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20190415</creationdate><title>The bands satisfying the strong isomorphism property</title><author>Yu, Baomin ; Zhao, Xianzhong</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c270t-9f050f17c9fb5369fdec29317fc8543c209d1ade1b6fdf8adb23360a3dbec1123</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2019</creationdate><topic>Algebra</topic><topic>Isomorphism</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Product development</topic><topic>Research Article</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Yu, Baomin</creatorcontrib><creatorcontrib>Zhao, Xianzhong</creatorcontrib><collection>CrossRef</collection><jtitle>Semigroup forum</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Yu, Baomin</au><au>Zhao, Xianzhong</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>The bands satisfying the strong isomorphism property</atitle><jtitle>Semigroup forum</jtitle><stitle>Semigroup Forum</stitle><date>2019-04-15</date><risdate>2019</risdate><volume>98</volume><issue>2</issue><spage>327</spage><epage>337</epage><pages>327-337</pages><issn>0037-1912</issn><eissn>1432-2137</eissn><abstract>The power semigroup, or global, of a semigroup
S
is the set
P
(
S
) of all nonempty subsets of
S
equipped with the naturally defined multiplication. A class
K
of semigroups is globally determined if any two semigroups of
K
with isomorphic globals are themselves isomorphic. A class
K
of semigroups is said to satisfy the strong isomorphism property if for each pair
S
,
T
∈
K
and each isomorphism
ψ
from
P
(
S
) onto
P
(
T
),
ψ
(
S
¯
)
=
T
¯
, where
S
¯
=
{
{
s
}
∣
s
∈
S
}
⊆
P
(
S
)
,
T
¯
=
{
{
t
}
∣
t
∈
T
}
⊆
P
(
T
)
, and hence
S
≅
T
. In this paper we investigate classes of bands satisfying the strong isomorphism property. We provide a description of the largest subclass
K
¯
of
K
satisfying the strong isomorphism property for a globally determined class
K
of semigroups, and give some characterizations of the members of
B
¯
for class
B
of all bands.</abstract><cop>New York</cop><pub>Springer US</pub><doi>10.1007/s00233-019-09998-9</doi><tpages>11</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0037-1912 |
| ispartof | Semigroup forum, 2019-04, Vol.98 (2), p.327-337 |
| issn | 0037-1912 1432-2137 |
| language | eng |
| recordid | cdi_proquest_journals_2186693385 |
| source | Springer Nature - Complete Springer Journals |
| subjects | Algebra Isomorphism Mathematics Mathematics and Statistics Product development Research Article |
| title | The bands satisfying the strong isomorphism property |
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