|
| 摘要: |
| 本文研究了扩展的有界分配格（即带有一个自同态运算的有界分配格）的次直不可约问题.利用不动点集和同余的方法，刻画了ep，qD代数类中次直不可约代数，获得了此类代数中有限次直不可约性和次直不可约性两者等价的结果，推广了Balbes以及Dwinger关于半格、分配格和布尔代数的相关结果. |
| 关键词: 扩展有界分配格 同余关系 次直不可约 |
| DOI： |
| 分类号:O153.1 |
| 基金项目:Supported by the Natural Science Found of Hubei Provence (2013CFB216). |
|
| DISTRIBUTIVE LATTICES WITH A HOMOMORPHIC OPERATION |
|
LUO Cong-wen,WANG Gao-xia
|
| Abstract: |
| In this paper, we initiate an investigation into the class eD of extended bounded distributive lattices, namely, bounded distributive lattices endowed with an unary operation, which is an endomorphism. By using the set of fixed points and congruences, we characterise the (finitely) subdirectly irreducible algebras in ep,qD. In particular, we show that for every algebra in ep,qD, the properties of being finitely subdirectly irreducible and subdirectly irreducible are equivalent. Some results obtained by Balbes and Dwinger on semilattices, distributive lattices and Boolean algebras are generalized. |
| Key words: extended bounded distributive lattice congruence subdirectly irreducible |
