带有同态运算的分配格（英文）  

DISTRIBUTIVE LATTICES WITH A HOMOMORPHIC OPERATION

作　　者：罗从文[1] 王高峡[1] LUO Cong-wen;WANG Gao-xia(College of Science,China Three Gorges University Yichang 443002,Chin)

机构地区：[1]三峡大学理学院,湖北宜昌443002

出　　处：《数学杂志》2018年第3期467-472,共6页Journal of Mathematics

基　　金：Supported by the Natural Science Found of Hubei Provence(2013CFB216)

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e_(p,q)D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.In this paper, we initiate an investigation into the class e D 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 e（p,q）D. In particular, we show that for every algebra in e（p,q）D,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.

关 键 词：扩展有界分配格 同余关系 次直不可约 

分 类 号：O153.1[理学—数学]