| Title:
|
Some module cohomological properties of Banach algebras (English) |
| Author:
|
Ilka, Elham |
| Author:
|
Mahmoodi, Amin |
| Author:
|
Bodaghi, Abasalt |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
145 |
| Issue:
|
2 |
| Year:
|
2020 |
| Pages:
|
127-140 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We find some relations between module biprojectivity and module biflatness of Banach algebras $\mathcal A$ and $\mathcal B$ and their projective tensor product $\mathcal A \mathbin {\widehat \otimes }\mathcal B$. For some semigroups $S$, we study module biprojectivity and module biflatness of semigroup algebras $l^{1}(S)$. (English) |
| Keyword:
|
module amenable |
| Keyword:
|
module biflat |
| Keyword:
|
module biprojective |
| Keyword:
|
semigroup algebra |
| MSC:
|
16E40 |
| MSC:
|
46H20 |
| MSC:
|
46H25 |
| idZBL:
|
07217185 |
| idMR:
|
MR4221825 |
| DOI:
|
10.21136/MB.2019.0055-17 |
| . |
| Date available:
|
2020-06-10T13:14:37Z |
| Last updated:
|
2021-04-19 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/148150 |
| . |
| Reference:
|
[1] Amini, M.: Module amenability for semigroup algebras.Semigroup Forum 69 (2004), 243-254 Corrigendum ibid. 72 2006 page 493. Zbl 1059.43001, MR 2081295, 10.1007/s00233-004-0107-3 |
| Reference:
|
[2] Amini, M., Bodaghi, A., Bagha, D. Ebrahimi: Module amenability of the second dual and module topological center of semigroup algebras.Semigroup Forum 80 (2010), 302-312. Zbl 1200.43001, MR 2601766, 10.1007/s00233-010-9211-8 |
| Reference:
|
[3] Bodaghi, A.: Module amenability of the projective module tensor product.Malay. J. Math. Sci. 52 (2011), 257-265. Zbl 1254.46051, MR 2854379 |
| Reference:
|
[4] Bodaghi, A., Amini, M.: Module character amenability of Banach algebras.Arch. Math. 99 (2012), 353-365. Zbl 1267.46062, MR 2990154, 10.1007/s00013-012-0430-y |
| Reference:
|
[5] Bodaghi, A., Amini, M.: Module biprojective and module biflat Banach algebras.Sci. Bull., Ser. A, Appl. Math. Phys., Politeh. Univ. Buchar. 75 (2014), 25-36. Zbl 1299.43002, MR 3130203 |
| Reference:
|
[6] Bodaghi, A., Amini, M., Babaee, R.: Module derivations into iterated dual of Banach algebras.Proc. Rom. Acad., Ser. A, Math. Phys. Tech. Sci. Inf. Sci. 12 (2011), 277-284. Zbl 1324.46060, MR 2870494 |
| Reference:
|
[7] Bodaghi, A., Ebrahimi, H., Bami, M. Lashkarizaheh: Generalized notions of module character amenability.Filomat 31 (2017), 1639-1654. MR 3635202, 10.2298/FIL1706639B |
| Reference:
|
[8] Bodaghi, A., Jabbari, A.: Module biflatness of the second dual of Banach algebras.Math. Rep., Buchar. 17 (2015), 235-247. Zbl 1374.46038, MR 3375731 |
| Reference:
|
[9] Dales, H. G.: Banach Algebras and Automatic Continuity.London Mathematical Society Monographs. New Series 24. Oxford University Press, Oxford (2000). Zbl 0981.46043, MR 1816726 |
| Reference:
|
[10] Duncan, J., Namioka, I.: Amenability of inverse semigroups and their semigroup algebras.Proc. R. Soc. Edinb., Sect. A 80 (1978), 309-321. Zbl 0393.22004, MR 0516230, 10.1017/S0308210500010313 |
| Reference:
|
[11] Essmaili, M., Medghalchi, A. R.: Biflatness of certain semigroup algebras.Bull. Iran. Math. Soc. 39 (2013), 959-969. Zbl 1300.43005, MR 3126267 |
| Reference:
|
[12] Grønbæk, N.: Biflatness and biprojectivity of Banach algebras graded over a semilattice.Glasg. Math. J. 52 (2010), 479-495. Zbl 1210.46037, MR 2679908, 10.1017/S0017089510000364 |
| Reference:
|
[13] İnceboz, H., Arslan, B., Bodaghi, A.: Module symmetrically amenable Banach algebra.Acta Math. Acad. Paedagog. Nyházi. (N.S.) 33 (2017), 233-245. MR 3896791 |
| Reference:
|
[14] Johnson, B. E.: Cohomology in Banach Algebras.Memoirs of the American Mathematical Society 127. AMS, Providence (1972). Zbl 0256.18014, MR 0374934, 10.1090/memo/0127 |
| Reference:
|
[15] Khelemskij, A. Ya.: Flat Banach modules and amenable algebras.Trudy Moskov. Mat. Obshch. 47 (1984), 179-218 Russian. Zbl 0569.46027, MR 0774950 |
| Reference:
|
[16] Bami, M. Lashkarizadeh, Valaei, M., Amini, M.: Super module amenability of inverse semigroup algebras.Semigroup Forum 86 (2013), 279-288. Zbl 1277.46022, MR 3034775, 10.1007/s00233-012-9432-0 |
| Reference:
|
[17] Pourmahmood-Aghababa, H.: (Super) module amenability, module topological center and semigroup algebras.Semigroup Forum 81 (2010), 344-356. Zbl 1207.46039, MR 2678721, 10.1007/s00233-010-9231-4 |
| Reference:
|
[18] Pourmahmood-Aghababa, H.: A note on two equivalence relations on inverse semigroups.Semigroup Forum 84 (2012), 200-202. Zbl 1242.20070, MR 2886007, 10.1007/s00233-011-9365-z |
| Reference:
|
[19] Pourmahmood-Aghbaba, H., Bodaghi, A.: Module approximate amenability of Banach algebras.Bull. Iran. Math. Soc. 39 (2013), 1137-1158. Zbl 1301.43002, MR 3145209 |
| Reference:
|
[20] Ramsden, P.: Biflatness of semigroup algebras.Semigroup Forum. 79 (2009), 515-530. Zbl 1213.43002, MR 2564061, 10.1007/s00233-009-9169-6 |
| Reference:
|
[21] Rezavand, R., Amini, M., Sattari, M. H., Bagha, D. Ebrahimi: Module Arens regularity for semigroup algebras.Semigroup Forum 77 (2008), 300-305 Corrigendum 79 2009 214-215. Zbl 1161.46026, MR 2443440, 10.1007/s00233-008-9075-3 |
| Reference:
|
[22] Rieffel, M. A.: Induced Banach representations of Banach algebras and locally compact groups.J. Func. Anal. 1 (1967), 443-491. Zbl 0181.41303, MR 0223496, 10.1016/0022-1236(67)90012-2 |
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