Amenability Modulo an Ideal of Second Duals of Semigroup Algebras
The aim of this paper is to investigate the amenability modulo, an ideal of Banach algebras with emphasis on applications to homological algebras. In doing so, we show that amenability modulo, an ideal of A * * implies amenability modulo, an ideal of A. Finally, for a large class of semigr...
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| Format: | Article |
| Language: | English |
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MDPI AG
2016-09-01
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| Series: | Mathematics |
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| Online Access: | http://www.mdpi.com/2227-7390/4/3/55 |
| _version_ | 1819052605870964736 |
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| author | Hamidreza Rahimi Khalil Nabizadeh |
| author_facet | Hamidreza Rahimi Khalil Nabizadeh |
| author_sort | Hamidreza Rahimi |
| collection | DOAJ |
| description | The aim of this paper is to investigate the amenability modulo, an ideal of Banach algebras with emphasis on applications to homological algebras. In doing so, we show that amenability modulo, an ideal of A * * implies amenability modulo, an ideal of A. Finally, for a large class of semigroups, we prove that l 1 ( S ) * * is amenable modulo I σ * * if and only if an appropriate group homomorphic image of S is finite, where I σ is the closed ideal induced by the least group congruence σ . |
| first_indexed | 2024-12-21T12:22:30Z |
| format | Article |
| id | doaj.art-5ede03c5fa71475db93518379da7df10 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-12-21T12:22:30Z |
| publishDate | 2016-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-5ede03c5fa71475db93518379da7df102022-12-21T19:04:17ZengMDPI AGMathematics2227-73902016-09-01435510.3390/math4030055math4030055Amenability Modulo an Ideal of Second Duals of Semigroup AlgebrasHamidreza Rahimi0Khalil Nabizadeh1Department of Mathematics, Faculty of Science, Central Tehran Branch, Islamic Azad University, P. O. Box 13185/768, Tehran, IranDepartment of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, IranThe aim of this paper is to investigate the amenability modulo, an ideal of Banach algebras with emphasis on applications to homological algebras. In doing so, we show that amenability modulo, an ideal of A * * implies amenability modulo, an ideal of A. Finally, for a large class of semigroups, we prove that l 1 ( S ) * * is amenable modulo I σ * * if and only if an appropriate group homomorphic image of S is finite, where I σ is the closed ideal induced by the least group congruence σ .http://www.mdpi.com/2227-7390/4/3/55amenability modulo an idealsemigroup algebragroup congruence |
| spellingShingle | Hamidreza Rahimi Khalil Nabizadeh Amenability Modulo an Ideal of Second Duals of Semigroup Algebras Mathematics amenability modulo an ideal semigroup algebra group congruence |
| title | Amenability Modulo an Ideal of Second Duals of Semigroup Algebras |
| title_full | Amenability Modulo an Ideal of Second Duals of Semigroup Algebras |
| title_fullStr | Amenability Modulo an Ideal of Second Duals of Semigroup Algebras |
| title_full_unstemmed | Amenability Modulo an Ideal of Second Duals of Semigroup Algebras |
| title_short | Amenability Modulo an Ideal of Second Duals of Semigroup Algebras |
| title_sort | amenability modulo an ideal of second duals of semigroup algebras |
| topic | amenability modulo an ideal semigroup algebra group congruence |
| url | http://www.mdpi.com/2227-7390/4/3/55 |
| work_keys_str_mv | AT hamidrezarahimi amenabilitymoduloanidealofseconddualsofsemigroupalgebras AT khalilnabizadeh amenabilitymoduloanidealofseconddualsofsemigroupalgebras |