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  1.  44
    Ockham Algebras with Balanced Double Pseudocomplementation.Jie Fang - 2008 - Studia Logica 90 (2):189-209.
    In this paper, we introduce a variety bdO of Ockham algebras with balanced double pseudocomplementation, consisting of those algebras of type where is an Ockham algebra, is a double p -algebra, and the operations and are linked by the identities [ f ( x )]* = [ f ( x )] + = f 2 ( x ), f ( x *) = x ** and f ( x + ) = x ++ . We give a description of the (...)
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  2.  24
    Congruences on a Balanced Pseudocomplemented Ockham Algebra Whose Quotient Algebras Are Boolean.Jie Fang & Lei-Bo Wang - 2010 - Studia Logica 96 (3):421-431.
    In this note we shall describe the lattice of the congruences on a balanced Ockham algebra with the pseudocomplementation whose quotient algebras are boolean. This is an extension of the result obtained by Rodrigues and Silva who gave a description of the lattice of congruences on an Ockham algebra whose quotient algebras are boolean.
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  3.  23
    Congruence Coherent Symmetric Extended de Morgan Algebras.T. S. Blyth & Jie Fang - 2007 - Studia Logica 87 (1):51-63.
    An algebra A is said to be congruence coherent if every subalgebra of A that contains a class of some congruence on A is a union of -classes. This property has been investigated in several varieties of lattice-based algebras. These include, for example, de Morgan algebras, p-algebras, double p-algebras, and double MS-algebras. Here we determine precisely when the property holds in the class of symmetric extended de Morgan algebras.
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  4.  10
    On Ideals and Congruences of Distributive Demi-P-Algebras.T. S. Blyth, Jie Fang & Leibo Wang - 2015 - Studia Logica 103 (3):491-506.
    We identify the \-ideals of a distributive demi-pseudocomplemented algebra L as the kernels of the boolean congruences on L, and show that they form a complete Heyting algebra which is isomorphic to the interval \ of the congruence lattice of L where G is the Glivenko congruence. We also show that the notions of maximal \-ideal, prime \-ideal, and falsity ideal coincide.
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  5.  9
    De Morgan Algebras with a Quasi-Stone Operator.T. S. Blyth, Jie Fang & Lei-bo Wang - 2015 - Studia Logica 103 (1):75-90.
    We investigate the class of those algebras in which is a de Morgan algebra, is a quasi-Stone algebra, and the operations \ and \ are linked by the identity x**º = x*º*. We show that such an algebra is subdirectly irreducible if and only if its congruence lattice is either a 2-element chain or a 3-element chain. In particular, there are precisely eight non-isomorphic subdirectly irreducible Stone de Morgan algebras.
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  6.  7
    The Lattice of Kernel Ideals of a Balanced Pseudocomplemented Ockham Algebra.Jie Fang, Lei-Bo Wang & Ting Yang - 2014 - Studia Logica 102 (1):29-39.
    In this note we shall show that if L is a balanced pseudocomplemented Ockham algebra then the set ${\fancyscript{I}_{k}(L)}$ of kernel ideals of L is a Heyting lattice that is isomorphic to the lattice of congruences on B(L) where ${B(L) = \{x^* | x \in L\}}$ . In particular, we show that ${\fancyscript{I}_{k}(L)}$ is boolean if and only if B(L) is finite, if and only if every kernel ideal of L is principal.
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  7. The Strong Endomorphism Kernel Property in Double MS-Algebras.Jie Fang - 2017 - Studia Logica 105 (5):995-1013.
    An endomorphism on an algebra \ is said to be strong if it is compatible with every congruence on \; and \ is said to have the strong endomorphism kernel property if every congruence on \, other than the universal congruence, is the kernel of a strong endomorphism on \. Here we characterise the structure of those double MS-algebras that have this property by the way of Priestley duality.
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