代数上的准同态及其应用

Pub Date : 2023-06-01 DOI:10.1142/s1005386723000160

X. Cao, S.H. Liu, X.S. Lu, Z.J. Ye, Z.R. Yu, Y.H. Zhang

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引用次数: 0

摘要

定义了派生和同态的新概念“非同态”。当一个非纯态是可逆的，它的逆就是一个Rota-Baxter算子。建立了非纯态的一般理论。得到了一个结合一元代数上所有非纯态的分类。与非平凡正导数的不存在性相反，证明了在完全有序域上的格序满矩阵代数和上三角矩阵代数上的任意对相反序上的非平凡正子纯态确实存在。

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Derimorphisms over Algebras and Applications

The new concept “derimorphism” generalizing both derivation and homomorphism is defined. When a derimorphism is invertible, its inverse is a Rota–Baxter operator. The general theory of derimorphism is established. The classification of all derimorphisms over an associative unital algebra is obtained. Contrary to the nonexistence of nontrivial positive derivations, it is shown that nontrivial positive derimorphisms do exist over any pair of opposite orderings over [Formula: see text], the lattice-ordered full matrix algebra and upper triangular matrix algebra over a totally ordered field.

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