let $mathcal{r}$ be a  commutative ring with identity, let $a$ and $b$ be two $mathcal{r}$-algebras and $varphi:blongrightarrow a$ be an $mathcal{r}$-additive algebra homomorphism. we introduce a new algebra $atimes_varphi b$, and give some basic properties of this algebra. generalized $2$-cocycle derivations on $atimes_varphi b$ are studied. accordingly, $atimes_varphi b$ is considered from th...

Let $mathcal{R}$ be a  commutative ring with identity, let $A$ and $B$ be two $mathcal{R}$-algebras and $varphi:Blongrightarrow A$ be an $mathcal{R}$-additive algebra homomorphism. We introduce a new algebra $Atimes_varphi B$, and give some basic properties of this algebra. Generalized $2$-cocycle derivations on $Atimes_varphi B$ are studied. Accordingly, $Atimes_varphi B$ is considered from th...

‎let $omega$ be a class of unital‎ ‎$c^*$-algebras‎. ‎we introduce the notion of a local tracial $omega$-algebra‎. ‎let $a$ be an $alpha$-simple unital local tracial $omega$-algebra‎. ‎suppose that $alpha:gto $aut($a$) is an action of a finite group $g$ on $a$‎ ‎which has a certain non-simple tracial rokhlin property‎. ‎then the crossed product algebra‎ ‎$c^*(g,a,alpha)$ is a unital local traci...

A Heyting algebra is a distributive lattice with implication and a dual $BCK$-algebra is an algebraic system having as models logical systems equipped with implication. The aim of this paper is to investigate the relation of Heyting algebras between dual $BCK$-algebras. We define notions of $i$-invariant and $m$-invariant on dual $BCK$-semilattices and prove that a Heyting semilattice is equiva...

Suppose that $A$ is a semi-simple and commutative Banach algebra. In this paper we try to characterize the character space of the Banach algebra $C_{rm{BSE}}(Delta(A))$ consisting of all  BSE-functions on $Delta(A)$ where $Delta(A)$ denotes the character space of $A$. Indeed, in the case that $A=C_0(X)$ where $X$ is a non-empty locally compact Hausdroff space, we give a complete characterizatio...

Renal Physiol 293: F1423–F1432, 2007 18. Shillingford JM, Piontek KB, Germino GG, Weimbs T: Rapamycin ameliorates PKD resulting from conditional inactivation of Pkd1. J Am Soc Nephrol 21: 489–497, 2010 19. Lieberthal W, Levine JS: The role of the mammalian target of rapamycin (mTOR) in renal disease. J Am Soc Nephrol 20: 2493–2502, 2009 20. Boehlke C, Kotsis F, Patel V, Braeg S, Voelker H, Bred...

1 Alonzo Church, Ann. Math., 2nd ser., 33, 346-366 (1932), and 34, 839-864 (1933). S. C. Kleene, Ann. Math., 2nd ser., 35, 529-544 (1934). We shall refer to the latter paper as Kleene 1934. 2 Alonzo Church and J. B. Rosser, "Some Properties of Conversion." 3 Explicit formal definitions are given by S. C. Kleene, Amer. Jour. Math., 57, 153173 (1935). This paper, and a second part of it, forthcom...

Gödel argued that intuition has an important role to play in mathematical epistemology, and despite the infamy of his own position, this opinion still has much to recommend it. Intuitions and folk platitudes play a central role in philosophical enquiry too, and have recently been elevated to a central position in one project for understanding philosophical methodology: the so-called ‘Canberra p...

In this paper, we introduce the notions of expansion of ideals in $MV$-algebras, $ (tau,sigma)- $primary, $ (tau,sigma)$-obstinate  and $ (tau,sigma)$-Boolean  in $ MV- $algebras. We investigate the relations of them. For example, we show that every $ (tau,sigma)$-obstinate ideal of an $ MV-$ algebra is $ (tau,sigma)$-primary  and $ (tau,sigma)$-Boolean. In particular, we define an expansion $ ...