@Article{,
author="",
title="Front Matter",
journal="Categories and General Algebraic Structures with Applications",
year="2013",
volume="1",
number="1",
pages="-",
abstract="",
issn="2345-5853",
doi="",
url="http://cgasa.sbu.ac.ir/article_4828.html"
}
@Article{Banaschewski2013,
author="Banaschewski, Bernhard",
title="Countable composition closedness and integer-valued continuous functions in pointfree topology",
journal="Categories and General Algebraic Structures with Applications",
year="2013",
volume="1",
number="1",
pages="1-10",
abstract="For any archimedean$f$-ring $A$ with unit in whichbreak$awedge (1-a)leq 0$ for all $ain A$, the following are shown to be equivalent: 1. $A$ is isomorphic to the $l$-ring ${mathfrak Z}L$ of all integer-valued continuous functions on some frame $L$. 2. $A$ is a homomorphic image of the $l$-ring $C_{Bbb Z}(X)$ of all integer-valued continuous functions, in the usual sense, on some topological space $X$. 3. For any family $(a_n)_{nin omega}$ in $A$ there exists an $l$-ring homomorphism break$varphi :C_{Bbb Z}(Bbb Z^omega)rightarrow A$ such that $varphi(p_n)=a_n$ for the product projections break$p_n:{Bbb Z^omega}rightarrow Bbb Z$. This provides an integer-valued counterpart to a familiar result concerning real-valued continuous functions.",
issn="2345-5853",
doi="",
url="http://cgasa.sbu.ac.ir/article_4262.html"
}
@Article{Dube2013,
author="Dube, Themba",
title="Concerning the frame of minimal prime ideals of pointfree function rings",
journal="Categories and General Algebraic Structures with Applications",
year="2013",
volume="1",
number="1",
pages="11-26",
abstract="Let $L$ be a completely regular frame and $mathcal{R}L$ be the ring of continuous real-valued functions on $L$. We study the frame $mathfrak{O}(Min(mathcal{R}L))$ of minimal prime ideals of $mathcal{R}L$ in relation to $beta L$. For $Iinbeta L$, denote by $textit{textbf{O}}^I$ the ideal ${alphainmathcal{R}Lmidcozalphain I}$ of $mathcal{R}L$. We show that sending $I$ to the set of minimal prime ideals not containing $textit{textbf{O}}^I$ produces a $*$-dense one-one frame homomorphism $beta Ltomathfrak{O}(Min(mathcal{R}L))$ which is an isomorphism if and only if $L$ is basically disconnected.",
issn="2345-5853",
doi="",
url="http://cgasa.sbu.ac.ir/article_4263.html"
}
@Article{Dube2013,
author="Dube, Themba
and Naidoo, Inderasan",
title="A pointfree version of remainder preservation",
journal="Categories and General Algebraic Structures with Applications",
year="2013",
volume="1",
number="1",
pages="27-58",
abstract=" Recall that a continuous function $fcolon Xto Y$ between Tychonoff spaces is proper if and only if the Stone extension $f^{beta}colon beta Xtobeta Y$ takes remainder to remainder, in the sense that $f^{beta}[beta X-X]subseteq beta Y-Y$. We introduce the notion of ``taking remainder to remainder" to frames, and, using it, we define a frame homomorphism $hcolon Lto M$ to be $beta$-proper, $lambda$-proper or $upsilon$-proper in case the lifted homomorphism $h^{beta}colonbeta Ltobeta M$, $h^{lambda}colonlambda Ltolambda M$ or $h^{upsilon}colonupsilon Ltoupsilon M$ takes remainder to remainder. These turn out to be weaker forms of properness. Indeed, every proper homomorphism is $beta$-proper, every $beta$-proper homomorphism is $lambda$-proper, and $lambda$-properness is equivalent to $upsilon$-properness. A characterization of $beta$-proper maps in terms of pointfree rings of continuous functions is that they are precisely those whose induced ring homomorphisms contract free maximal ideals to free prime ideals.",
issn="2345-5853",
doi="",
url="http://cgasa.sbu.ac.ir/article_4264.html"
}
@Article{Gould2013,
author="Gould, Victoria
and Zenab, Rida-e-",
title="Semigroups with inverse skeletons and Zappa-Sz$\acute{\rm e}$p products",
journal="Categories and General Algebraic Structures with Applications",
year="2013",
volume="1",
number="1",
pages="59-89",
abstract="The aim of this paper is to study semigroups possessing $E$-regular elements, where an element $a$ of a semigroup $S$ is {em $E$-regular} if $a$ has an inverse $a^\circ$ such that $aa^\circ,a^\circ a$ lie in $ E\subseteq E(S)$. Where $S$ possesses `enough' (in a precisely defined way) $E$-regular elements, analogues of Green's lemmas and even of Green's theorem hold, where Green's relations ${\mathcal R},{\mathcal L},{\mathcal H}$ and $\mathcal D$ are replaced by $\widetilde{{\mathcal R}}_E,\widetilde{{\mathcal L}}_E, \widetilde{{\mathcal H}}_E$ and $\widetilde{\mathcal{D}}_E$. Note that $S$ itself need not be regular. We also obtain results concerning the extension of (one-sided) congruences, which we apply to (one-sided) congruences on maximal subgroups of regular semigroups. If $S$ has an inverse subsemigroup $U$ of $E$-regular elements, such that $E\subseteq U$ and $U$ intersects every $\widetilde{{\mathcal H}}_E$-class exactly once, then we say that $U$ is an {em inverse skeleton} of $S$. We give some natural examples of semigroups possessing inverse skeletons and examine a situation where we can build an inverse skeleton in a $\widetilde{\mathcal{D}}_E$-simple monoid. Using these techniques, we show that a reasonably wide class of $\widetilde{\mathcal{D}}_E$-simple monoids can be decomposed as Zappa-Sz$\acute{\rm e}$p products. Our approach can be immediately applied to obtain corresponding results for bisimple inverse monoids.",
issn="2345-5853",
doi="",
url="http://cgasa.sbu.ac.ir/article_4265.html"
}
@Article{He2013,
author="He, Wei",
title="A note on semi-regular locales",
journal="Categories and General Algebraic Structures with Applications",
year="2013",
volume="1",
number="1",
pages="91-101",
abstract="Semi-regular locales are extensions of the classical semiregular spaces. We investigate the conditions such that semi-regularization is a functor. We also investigate the conditions such that semi-regularization is a reflection or coreflection.",
issn="2345-5853",
doi="",
url="http://cgasa.sbu.ac.ir/article_4266.html"
}
@Article{Zhang2013,
author="Zhang, Xia
and Zhang, Wenling
and Knauer, Ulrich",
title="A characterization of a pomonoid $S$ all of its cyclic $S$-posets are regular injective",
journal="Categories and General Algebraic Structures with Applications",
year="2013",
volume="1",
number="1",
pages="103-117",
abstract="This work is devoted to give a charcaterization of a pomonoid $S$ such that all cyclic $S$-posets are regular injective.",
issn="2345-5853",
doi="",
url="http://cgasa.sbu.ac.ir/article_4267.html"
}
@Article{,
author="",
title="Persian Abstracts",
journal="Categories and General Algebraic Structures with Applications",
year="2013",
volume="1",
number="1",
pages="-",
abstract="",
issn="2345-5853",
doi="",
url="http://cgasa.sbu.ac.ir/article_4829.html"
}