Abstract
In this paper, we first introduce the notion of Stonean implicative filter in Hilbert algebra and study it in detail. Finally, we introduce a Stonean Hilbert algebra and investigate its properties, we prove that,
Get full access to this article
View all access options for this article.
References
1.
Buşneag
D.
, Categories of algebraic logic , Ed. Academiei Române , 2006 .
2.
Buşneag
D.
, On the maximal deductive system of a bounded Hilbert algebra , Bull Math Soc Sci Math Roumanie, Tome 31 ((79),1 ) (1987 ), 9 –21 .
3.
Buşneag
D.
and
Ghita
M.
, Some latticial properties of Hilbert algebras , Bull Math Soc Sci Math Roumanie Tome 53 ((101) (2) ) (2010 ), 87 –107 .
4.
Celani
S.A.
, α-ideal and α-deductive systems in bounded hilbert algebras , J of Mult valued Logic and Soft Computing (2013 ), 1 –18 .
5.
Celani
S.A.
and
Montangie
D.
, Hilbert algebras with supremum , Algebra Universalis 67 (2012 ), 237 –255 .
6.
Dan
C.
, Hilbert algebras of fractions , Int J Math and Math Sci (2009 ), 16 . Article ID 589830 .
7.
Diego
A.
, Sur les algebres de Hilbert , Collection de Logique Mathematique , Edition Hermann , Serie A, XXI , 1966 .
8.
Figallo
A.V.
and
Ziliani
A.
, Remarks on Hertz algebras and implicative semi- lattices , Bulletin of the Sectio Logic 34/1 (2005 ), 37 –42 .
9.
Figallo
A.V.
,
Ramon
G.Z.
and
Saad
S.
, A note on the Hilbert algebras with infimum , Math Contemp 24 (2003 ), 23 –37 .
10.
Hong
S.M.
and
Jun
Y.B.
, On deductive systems of Hilbert algebras , Comm Korean Math Soc 11 (3 ) (1996 ), 595 –600 .
11.
Idziak
P.M.
, Lattice operations in BCK-algebras , Math Japonica 29 (6 ) (1984 ), 839 –846 .
12.
Jun
Y.B.
,
Kim
S.Y.
and
Roh
E.H.
, The abysm of a Hilbert algebra , Sci Math Jpn 65 (1 ) (2007 ), 135 –140 .
13.
Muresan
C.
, Dense elements and classes of residuated lattices , Bull Math Soc Sci Math Roumanie Tome 53 ((101) (1) ) (2010 ), 11 –24 .
14.
Piciu
D.
, Algebras of fuzzy logic , Ed. Universitaria, Craiova , 2007 .
15.
Porta
H.
, Sur quelques algèbres de la Logique , Portugaliae Mathematica 40 (Fasc 1 ) (1981 ), 41 –77 .
16.
Rasiowa
H.
, An algebraic approach to non-classical logics, Stud. in Logic, 78 , North Holland, Amsterdam , 1974 .
17.
Soleimani Nasab
A.
and
Borumand Saeid
A.
, Implication Hilbert algebra , submitted .
18.
Soleimani Nasab
A.
and
Borumand Saeid
A.
, Semi maximal filter in Hilbert algebra , Journal of Intelligent and Fuzzy Systems (to appear) .
19.
Soleimani Nasab
A.
and
Borumand Saeid
A.
, Some results in to local Hilbert algebras, Math. Slovaca (to appear).
20.
Soleimani Nasab
A.
and
Borumand Saeid
A.
, Study of Hilbert algebras in point of filters , An Şt. Univ. Ovidius Constanţa (to appear) .
21.
Turunen
E.
, Boolean deductive Systems of BL-algebras , Arch Math Logic 40 (2001 ), 467 –473 .