On direct sums in bounded BCK-algebras
Commun. Korean Math. Soc. 2005 Vol. 20, No. 2, 221-229
Printed June 1, 2005
Yisheng Huang
Sanming College
Abstract : In this paper we consider the decompositions of subdirect sums and direct sums in bounded BCK-algebras. The main results are as follows. Given a bounded BCK-algebra $X$, if $X$ can be decomposed as the subdirect sum $\overline{\bigoplus}_{i\in I}A_i$ of a nonzero ideal family $\{A_i\mid i\in I\}$ of $X$, then $I$ is finite, every $A_i$ is bounded, and $X$ is embeddable in the direct sum $\bigoplus_{i\in I}A_i$; if $X$ is with condition (S), then it can be decomposed as the subdirect sum $\overline{\bigoplus}_{i\in I}A_i$ if and only if it can be decomposed as the direct sum $\bigoplus_{i\in I}A_i$; if $X$ can be decomposed as the direct sum $\bigoplus_{i\in I}A_i$, then it is isomorphic to the direct product $\prod_{i\in I}A_i$.
Keywords : bounded BCK-algebra, ideal, subdirect sum, direct sum, direct product
MSC numbers : 06F35
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