关于Plonka和与正则化品种的一些代数性质
On some algebraic properties of Plonka sums and regularized varieties
AI总结：
本文研究了Plonka和与正则化品种的代数性质，扩展了相关结果并揭示了子品种格中的分裂特性。
摘要：
Płonka和是一种通用构造，为正则化品种中的代数提供了结构描述，其例子从Clifford半群到许多逻辑代数，包括involutive bisemilattices、Bochvar代数和某些余 residuated 结构。虽然对于没有常数的多重类型，子直接不可约代数、子品种格和自由代数等性质已被深入研究，但一般情况下涉及零元运算的情况仍鲜有探索。本文将这些结果扩展到具有常数的代数类型，并在正则化品种的子品种格中提供新的关于分裂的见解。此外，我们还对Płonka和的同余关系进行了完整刻画，并证明了该构造保持了满射同态和单射满射。
英文摘要：
Płonka sums consist of a general construction that provides structural description for algebras in regularized varieties, whose examples range from Clifford semigroups to many algebras of logic including involutive bisemilattices, Bochvar algebras and certain residuated structures. While properties such as subdirectly irreducible algebras, subvariety lattices, and free algebras are well-understood for plural types without constants, the general case involving nullary operations remains largely unexplored. In this paper, we extend these results to algebraic types with constants and provide new insights into splittings within the lattice of subvarieties of a regularized variety. Furthermore, we offer a complete characterization of the congruences of a Płonka sum and establish that the construction preserves surjective epimorphisms and injective monomorphisms.
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。
