全序化不变映射的更简单刻画
Simpler characterizations of total orderization invariant maps
AI总结：
针对分配格上全序化不变映射研究中全序化符号繁琐导致计算困难的问题，本文给出全序化映射的更简单刻画，证明格多同态全序化不变当且仅当对称，且对称格多同态的对角线是格同态，推广了向量格相关已知结果。
摘要：
给定分配格的有限子集$A$，其全序化$to(A)$是将$A$转化为全序集的自然变换。近期，作者证明了在全序化下保持不变的分配格上多元映射，可推广向量格上的多种映射，包括有界正交对称多重线性映射以及有界正交可加多项式的有限和。因此，对分配格上全序化不变映射的研究，为向量格理论中被广泛研究的映射提供了新视角。然而，全序化繁琐的符号会使计算变得极为冗长困难。本文通过给出全序化映射的简洁得多的刻画，解决了这一难题。利用这些更简便的表示，我们随后证明了分配格上的格多同态是全序化不变的，当且仅当它是对称的；同时我们证明了对称格多同态的对角线是格同态，推广了正交对称向量格同态的已知结果。
英文摘要：
Given a finite subset $A$ of a distributive lattice, its total orderization $to(A)$ is a natural transformation of $A$ into a totally ordered set. Recently, the author showed that multivariate maps on distributive lattices which remain invariant under total orderizations generalize various maps on vector lattices, including bounded orthosymmetric multilinear maps and finite sums of bounded orthogonally additive polynomials. Therefore, a study of total orderization invariant maps on distributive lattices provides new perspectives for maps widely researched in vector lattice theory. However, the unwieldy notation of total orderizations can make calculations extremely long and difficult. In this paper we resolve this complication by providing considerably simpler characterizations of total orderization maps. Utilizing these easier representations, we then prove that a lattice multi-homomorphism on a distributive lattice is total orderization invariant if and only if it is symmetric, and we show that the diagonal of a symmetric lattice multi-homomorphism is a lattice homomorphism, extending known results for orthosymmetric vector lattice homomorphisms.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
