Complete congruence lattices of two related modular lattices

Gábor Czédli

摘要

AbstractBy a 1991 result of R. Freese, G. Gr?tzer, and E. T. Schmidt, every complete latticeAis isomorphic to the lattice Com(K) of complete congruences of a strongly atomic, 3-distributive, complete modular latticeK. In 2002, Gr?tzer and Schmidt improved 3-distributivity to 2-distributivity. Here, we represent morphisms between two complete lattices with complete lattice congruences in three ways. Namely, for$${i in {1, 2, 3},}$$

i \in {1, 2, 3},

let$${A_i}$$

A_{i}

and$${A^{prime}_{i}}$$

A_{i}^{'}

be arbitrary complete lattices and let$${f_i}$$

f_{i}

:$${A_{i} ightarrow A^{prime}_{i}}$$

A_{i} \to A_{i}^{'}

be maps such that (i)$${f_1}$$

f_{1}

is$${(igvee, 0)}$$

(?, 0)

-preserving and 0-separating, (ii)$${f_2}$$

机译：[CDATA [<标题>抽象 <帕拉> R.Freese，G. GR吗？TZER和ET SCHMIDT的1991年，每个完整的格子<重点类型=“斜体”> 与晶格相同（<重点类型=“斜体”> k ）的完全同时的强烈，3分配，完整的模块化格子<重点类型=“斜体”> K 。 2002年，GR？TERD和SCHMIDT改善了3分发电量分配。在这里，我们在三种方式中代表两个完整的格子与完整的格子同时之间的态度。即，对于 < arequationsource格式=“tex”> $$ {i in {1,2,3 }，} $$

i\in{1，2，3} ，< / mo>Let$$ {a_i} $$ ai$$ {a ^ { prime} _ {i $$ a< mi> i''是任意完整的格子，让$$ {f_i} $$ fi：$$ {a _ {i}  lightarrow a ^ { prime} _ {i}} $$ AI\to

Complete congruence lattices of two related modular lattices

摘要

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