@article { author = {Borzooei, Rajabali and Mohseni Takallo, M. and Jun, Young Bae and Aaly Kologani, M.}, title = {Positive implicative True-False ideals in BCK-algebras}, journal = {Journal of Mahani Mathematical Research}, volume = {11}, number = {3}, pages = {69-85}, year = {2022}, publisher = {Shahid Bahonar University of Kerman}, issn = {2251-7952}, eissn = {2645-4505}, doi = {10.22103/jmmrc.2022.19150.1216}, abstract = {In BCK-algebra, the concept of  a positive implicative $T\&F$-ideal is introduced, and further several properties are  investigated. The relationship between  $T\&F$-ideals and  positive implicative $T\&F$-ideals is established, and an example is given to reveal that  a $T\&F$-ideal is not a positive implicative $T\&F$-ideal. Various conditions under which  a $T\&F$-ideal can be a positive implicative $T\&F$-ideal are explored and various characterizations of a positive  implicative $T\&F$-ideal are studied. The extended property of a positive implicative $T\&F$-ideal is constructed.}, keywords = {True-False structure,(limited) $T&F$-ideal,(limited) positive implicative $T&F$-ideal}, url = {https://jmmrc.uk.ac.ir/article_3324.html}, eprint = {https://jmmrc.uk.ac.ir/article_3324_652488ba4bd146fb12cd6ec1e9153911.pdf} }