| Title:
|
Radical decompositions of semiheaps (English) |
| Author:
|
Hawthorn, Ian |
| Author:
|
Stokes, Tim |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
50 |
| Issue:
|
2 |
| Year:
|
2009 |
| Pages:
|
191-208 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Semiheaps are ternary generalisations of involuted semigroups. The first kind of semiheaps studied were heaps, which correspond closely to groups. We apply the radical theory of varieties of idempotent algebras to varieties of idempotent semiheaps. The class of heaps is shown to be a radical class, as are two larger classes having no involuted semigroup counterparts. Radical decompositions of various classes of idempotent semiheaps are given. The results are applied to involuted I-semigroups, leading to a radical-theoretic interpretation of the largest idempotent-separating congruence. (English) |
| Keyword:
|
radical theory of idempotent algebras |
| Keyword:
|
ternary operation |
| Keyword:
|
involuted semigroups |
| Keyword:
|
semiheaps |
| Keyword:
|
generalised heaps |
| Keyword:
|
heaps |
| MSC:
|
20M11 |
| MSC:
|
20N10 |
| idZBL:
|
Zbl 1204.20087 |
| idMR:
|
MR2537831 |
| . |
| Date available:
|
2009-08-18T12:24:34Z |
| Last updated:
|
2013-09-22 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/133428 |
| . |
| Reference:
|
[1] Baer R.: Zür Einfuhrung des Scharbegriffs.J. Reine Angew. Math. 160 (1929), 199--207. |
| Reference:
|
[2] Divinsky N.: Rings and Radicals.Allen and Unwin, 1965. Zbl 0138.26303, MR 0197489 |
| Reference:
|
[3] Gardner B.J.: Radical decompositions of idempotent algebras.J. Austral Math. Soc. (Series A) 36 (1984), 213--236. Zbl 0541.08001, MR 0725747, 10.1017/S1446788700024666 |
| Reference:
|
[4] Hoehnke H.-J.: Radikale in allgemeinen Algebren.Math. Nachr. 32 (1966), 347--383. Zbl 0149.02003, MR 0227077, 10.1002/mana.19660320607 |
| Reference:
|
[5] Hoehnke H.-J.: Einige neue Resultate über abstrakte Halbgruppen.Colloq. Math. 14 (1966), 329--349. Zbl 0196.29501, MR 0185027 |
| Reference:
|
[6] Howie J.M.: The maximum idempotent separating congruence on an inverse semigroup.Proc. Edinburgh Math. Soc. 14 (1964/65), 71--79. MR 0163976 |
| Reference:
|
[7] Howie J.M.: Fundamentals of Semigroup Theory.Oxford University Press, Oxford, 1995. Zbl 0835.20077, MR 1455373 |
| Reference:
|
[8] Márki L., Mlitz R., Wiegandt R.: A General Kurosh-Amitsur radical theory.Comm. Algebra 16 (1988), 249--305. MR 0929120, 10.1080/00927878808823572 |
| Reference:
|
[9] Munn W.D.: Fundamental Inverse Semigroups.Quart. J. Math. Oxford Ser. (2) 17 (1966), 157--170. Zbl 0219.20047, MR 0262402 |
| Reference:
|
[10] Prüfer H.: Theorie der Abelschen Gruppen.Math. Z. 20 (1924), 165--187. MR 1544670, 10.1007/BF01188079 |
| Reference:
|
[11] Stokes T.: Radical classes of algebras with B-action.Algebra Universalis 40 (1998), 73--85. Zbl 0935.08004, MR 1643221, 10.1007/s000120050082 |
| Reference:
|
[12] Vagner V.V.: The theory of generalized heaps and generalized groups.(Russian), Mat. Sbornik N.S. 32 (1953), 545--632. MR 0059267 |
| . |
