Decompositions of a C

We prove that if A is a C-algebra, then for each a∈A, Aa={x∈A/x≤a} is itself a C-algebra and is isomorphic to the quotient algebra A/θa of A where θa={(x,y)∈A×A/a∧x=a∧y}. If A is C-algebra with T, we prove that for every a∈B(A), the centre of A, A is isomorphic to Aa×Aa′ and that if A is isomorphic A1×A2, then there exists a∈B(A) such that A1 is isomorphic Aa and A2 is isomorphic to Aa′. Using this decomposition theorem, we prove that if a,b∈B(A) with a∧b=F, then Aa is isomorphic to Ab if and only if there exists an isomorphism φ on A such that φ(a)=b

Boolean Algebra of C-Algebras

A C- algebra is the algebraic form of the 3-valued conditional logic, which was introduced by F. Guzman and C. C. Squier in 1990. In this paper, some equivalent conditions for a C- algebra to become a boolean algebra in terms of congruences are given. It is proved that the set of all central elements B(A) is isomorphic to the Boolean algebra of all C-algebras Sa, where a B(A). It is also proved that B(A) is isomorphic to the Boolean algebra of all C-algebras Aa, where a B(A)

Boolean Centre of a C-algebra

There is a precise characterisation of factor congruences on a C-algebra with meet identity $T$. The characterisation of such congruences on a C-algebra with out $T$ is a difficult task. In this paper, we make such an attempt and we characterise the factor congruences on a C-algebra $A$ and identify these with certain elements or sets of elements of $A$

Spin-reorientation, ferroelectricity and magnetodielectric effect in YFe_1−x Mn_xO₃ (0.1 ≤ x ≤ 0.40)

We report the observation of magnetoelectric and magnetodielectric effects at different temperatures in Mn-substituted yttrium orthoferrite, YFe_1−x Mn_xO₃ (0.1 ≤ x ≤ 0.40). Substitution of Mn in antiferromagnetic YFeO₃ (T_N = 640  K) induces a first-order spin-reorientation transition at a temperature, T_SR, which increases with x whereas the Neel temperature (T_N) decreases. While the magnetodielectric effect occurs at T_SR and T_N, the ferroelectricity appears rather at low temperatures. The origin of magnetodielectric effect is attributed to spin-phonon coupling as evidenced from the temperature dependence of Raman phonon modes. The large magnetocapacitance (18% at 50 kOe) near T_SR = 320  K and high ferroelectric transition temperature (∼115  K) observed for x = 0.4 suggest routes to enhance magnetoelectric effect near room temperature for practical applications

Structure and complex magnetic behavior of disordered perovskite (Bi<SUB>0.5</SUB>Sr<SUB>0.5</SUB>)(Fe<SUB>0.5</SUB>Mn<SUB>0.5</SUB>)O<SUB>3</SUB>

Bi0.5Sr0.5)(Fe0.5Mn0.5)O3 crystallizes in a rhombohedral structure, with space group R3c, where the cations Bi3+/Sr2+ and Fe3+/Mn4+ occupy 6a and 6b sites respectively. Neutron diffraction, Mossbauer and magnetization measurements confirm long range antiferromagnetic ordering of the Fe3+ and Mn4+ moments at TN (226 K). Below TN, this oxide exhibits a cluster glass behavior and at low temperatures (~30 K) a spin glass state is observed. The complex magnetic behavior is attributed to cation disorder in the system. Magnetic properties of this oxide are compared with those of the isostructural Bi0.5La0.5Fe0.5Mn0.5O3 where both Fe and Mn ions exist in trivalent state