ON SEMI MAXIMAL FILTERS IN BL-ALGEBRAS

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PAAD A.; BORZOOEI R.A.

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Journal: JOURNAL OF ALGEBRAIC SYSTEMS Year:2019 | Volume:6 | Issue:2 Page(s): 101-116

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Information Journal Paper

Title

ON SEMI MAXIMAL FILTERS IN BL-ALGEBRAS

Author(s)

PAAD A. | BORZOOEI R.A. | Issue Writer Certificate

Keywords

(Semi simple)BL-algebra

G¨odel algebra

semi maximal filter

radical of filter

Abstract

In this paper, first we study the semi maximal filters in linear BL-algebras and we prove that any semi maximal filter is a primary filter. Then, we investigate the radical of semi maximal filters in BL-algebras. Moreover, we determine the relationship between this filters and other types of filters in BL-algebras and G¨ odel algebra. Specially, we prove that in a G¨ odel algebra, any fantastic filter is a semi maximal filter and any semi maximal filter is an (n-fold) positive implicative filter. Also, in a BL-algebra, any semi maximal and implicative filter is a positive implicative filter. Finally, we give an answer to the open problem in [S. Motamed, L. Torkzadeh, A. Borumand Saeid and N. Mohtashamnia, radical of filters in BL-algebras, Math. Log. Quart. 57, No. 2, (2011), 166-179 ].

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APA: Copy

PAAD, A., & BORZOOEI, R.A.. (2019). ON SEMI MAXIMAL FILTERS IN BL-ALGEBRAS. JOURNAL OF ALGEBRAIC SYSTEMS, 6(2 ), 101-116. SID. https://sid.ir/paper/268400/en

Vancouver: Copy

PAAD A., BORZOOEI R.A.. ON SEMI MAXIMAL FILTERS IN BL-ALGEBRAS. JOURNAL OF ALGEBRAIC SYSTEMS[Internet]. 2019;6(2 ):101-116. Available from: https://sid.ir/paper/268400/en

IEEE: Copy

A. PAAD, and R.A. BORZOOEI, “ON SEMI MAXIMAL FILTERS IN BL-ALGEBRAS,” JOURNAL OF ALGEBRAIC SYSTEMS, vol. 6, no. 2 , pp. 101–116, 2019, [Online]. Available: https://sid.ir/paper/268400/en

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