Geodesic
Z • −ideals in MV−algebras of continuous functions
Filomat, Tome 36 (2022) no. 7, p. 2439

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DOI

In this paper, we study MV−algebra of continuous functions C(X) and maximal ideals of C(X). Furthermore, Z−ideal and Z • −ideal of C(X) are introduced and proved that every Z • −ideal in C(X) is a Z−ideal but the converse is not true and every finitely generated Z−ideal is a basic Z • −ideal. Also, we investigate meet and join of two Z−ideals (Z • −ideal) of C(X). Complemented elements of C(X) are examined and their properties have been studied. In particular, the relationship between generated ideal by them and Z−ideals (Z • −ideals) is proved. Finally, we investigate some property of Z • −ideals in basically disconnected space and extremally disconnected space.
DOI : 10.2298/FIL2207439B
Classification : 06D35, 06B10, 54C05
Keywords: MV-algebra, (Z◦, Z)ideal, zero divisor, complemented element 
Mahta Bedrood; Farhad Sajadian; Arsham Boru; and Saeid. Z • −ideals in MV−algebras of continuous functions. Filomat, Tome 36 (2022) no. 7, p. 2439 . doi: 10.2298/FIL2207439B
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     author = {Mahta Bedrood and Farhad Sajadian and Arsham Boru and and Saeid},
     title = {Z {\textbullet} \ensuremath{-}ideals in {MV\ensuremath{-}algebras} of continuous functions},
     journal = {Filomat},
     pages = {2439 },
     year = {2022},
     volume = {36},
     number = {7},
     doi = {10.2298/FIL2207439B},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2207439B/}
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