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On weak-BCC-algebras.

Janus Thomys1, Xiaohong Zhang

  • 1Institute of Mathematics, Wroclaw University of Technology, 50-370 Wroclaw, Poland.

Thescientificworldjournal
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Summary
This summary is machine-generated.

This study introduces weak-BCC-algebras (BZ-algebras) with a restricted associative property. Researchers characterized their ideals, nilradicals, and nilpotent elements.

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Area of Science:

  • Algebraic Structures
  • Abstract Algebra

Background:

  • BCC-algebras are algebraic structures with specific properties.
  • BZ-algebras are a type of BCC-algebra.

Purpose of the Study:

  • Introduce and define weak-BCC-algebras (BZ-algebras).
  • Investigate the specific condition (x∗y)∗z = (x∗z)∗y in these algebras.
  • Characterize algebraic properties like ideals, nilradicals, and nilpotent elements.

Main Methods:

  • Definition of weak-BCC-algebras based on a modified associative property.
  • Analysis of the structure of these algebras.
  • Characterization of ideals, nilradicals, and nilpotent elements within the defined algebraic framework.

Main Results:

  • Formal definition of weak-BCC-algebras (BZ-algebras).
  • Identification of the specific condition under which the property (x∗y)∗z = (x∗z)∗y holds.
  • Characterization of ideals, nilradicals, and nilpotent elements in weak-BCC-algebras.

Conclusions:

  • Weak-BCC-algebras present a variation of BCC-algebras with a branch-dependent property.
  • The study provides a foundational understanding of these algebras and their key components.