| Title:
|
Standard and distributive ideals in trellises (English) |
| Author:
|
Bhargava, K. |
| Author:
|
Hegde, Chandru |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0011-4642 |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
151 |
| Issue:
|
4 |
| Year:
|
2026 |
| Pages:
|
573-585 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The concept of standard ideals in lattices, introduced by G. Grätzer and E. T. Schmidt, plays a significant role in the development of lattice theory. It serves as a generalization of normal subgroups in groups and ideals in rings to lattices. Similarly, the notion of distributive ideals, introduced by O. Ore, is another important tool in lattice theory. Building on these ideas, we extend the concepts of standard ideals and distributive ideals to the broader context of trellises. A trellis is a pseudo-ordered set where every pair of elements has both the least upper bound and the greatest lower bound. Within this framework, many of the results of Grätzer and Schmidt are effectively generalized to trellises. (English) |
| Keyword:
|
trellis |
| Keyword:
|
weakly-associative lattice |
| Keyword:
|
pseudo-ordered set |
| Keyword:
|
standard ideal |
| Keyword:
|
distributive ideal |
| Keyword:
|
congruence relation |
| MSC:
|
06A75 |
| MSC:
|
06B10 |
| MSC:
|
06B75 |
| DOI:
|
10.21136/MB.2025.0025-25 |
| . |
| Date available:
|
2026-09-23T08:23:09Z |
| Last updated:
|
2026-09-23 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/153767 |
| . |
| Reference:
|
[1] Bhatta, S. P., Ramananda, H. S.: On ideals and congruence relations in trellises.Acta Math. Univ. Comen., New Ser. 79 (2010), 209-216. Zbl 1240.06018, MR 2745169 |
| Reference:
|
[2] Fried, E.: Tournaments and non-associative lattices.Ann. Univ. Sci. Budap. Rolando Eötvös, Sect. Math. 13 (1970), 151-164. Zbl 0224.06004, MR 0321837 |
| Reference:
|
[3] Grätzer, G.: General Lattice Theory.Birkhäuser, Basel (1978). Zbl 0385.06015, MR 0504338, 10.1007/978-3-0348-7633-9 |
| Reference:
|
[4] Grätzer, G., Schmidt, E. T.: Standard ideals in lattices.Acta Math. Acad. Sci. Hung. 12 (1961), 17-86. Zbl 0115.01901, MR 0133265, 10.1007/BF02066675 |
| Reference:
|
[5] Rai, S. B.: Distributive, standard and neutral elements in trellises.Acta Math. Univ. Comen., New Ser. 77 (2008), 167-174. Zbl 1174.06004, MR 2489188 |
| Reference:
|
[6] Skala, H. L.: Trellis theory.Algebra Univers. 1 (1971), 218-233. Zbl 0242.06003, MR 0302523, 10.1007/BF02944982 |
| Reference:
|
[7] Skala, H.: Trellis Theory.Memoirs of the American Mathematical Society 121. AMS, Providence (1972). Zbl 0242.06004, MR 0325474, 10.1090/memo/0121 |
| . |
