@article {
author = {},
title = {Front Matter},
journal = {Categories and General Algebraic Structures with Applications},
volume = {1},
number = {1},
pages = {-},
year = {2013},
publisher = {Shahid Beheshti University},
issn = {2345-5853},
eissn = {2345-5861},
doi = {},
abstract = {},
keywords = {},
url = {https://cgasa.sbu.ac.ir/article_4828.html},
eprint = {https://cgasa.sbu.ac.ir/article_4828_41e2214bc1c00610f598b8812deba79c.pdf}
}
@article {
author = {Banaschewski, Bernhard},
title = {Countable composition closedness and integer-valued continuous functions in pointfree topology},
journal = {Categories and General Algebraic Structures with Applications},
volume = {1},
number = {1},
pages = {1-10},
year = {2013},
publisher = {Shahid Beheshti University},
issn = {2345-5853},
eissn = {2345-5861},
doi = {},
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.},
keywords = {Frames,0-dimensional frames,integer-valued continuous
functions on frames,archimedean ${mathbb Z}$-rings,countable
$mathbb {Z}$-composition closedness},
url = {https://cgasa.sbu.ac.ir/article_4262.html},
eprint = {https://cgasa.sbu.ac.ir/article_4262_73b32f9f16cd67536694bb804916b55f.pdf}
}
@article {
author = {Dube, Themba},
title = {Concerning the frame of minimal prime ideals of pointfree function rings},
journal = {Categories and General Algebraic Structures with Applications},
volume = {1},
number = {1},
pages = {11-26},
year = {2013},
publisher = {Shahid Beheshti University},
issn = {2345-5853},
eissn = {2345-5861},
doi = {},
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.},
keywords = {frame,ring of real-valued continuous functions on a
frame,minimal prime ideal,basically disconnected},
url = {https://cgasa.sbu.ac.ir/article_4263.html},
eprint = {https://cgasa.sbu.ac.ir/article_4263_6f79ee547811c22128d166583042a1da.pdf}
}
@article {
author = {Dube, Themba and Naidoo, Inderasan},
title = {A pointfree version of remainder preservation},
journal = {Categories and General Algebraic Structures with Applications},
volume = {1},
number = {1},
pages = {27-58},
year = {2013},
publisher = {Shahid Beheshti University},
issn = {2345-5853},
eissn = {2345-5861},
doi = {},
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.},
keywords = {frame,remainder preservation,Stone-v{Cech} compactification,regular Lindel"{o}f coreflection,realcompact coreflection,proper map,lax proper map},
url = {https://cgasa.sbu.ac.ir/article_4264.html},
eprint = {https://cgasa.sbu.ac.ir/article_4264_91ce60eb77415d9197885588177906a7.pdf}
}
@article {
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},
volume = {1},
number = {1},
pages = {59-89},
year = {2013},
publisher = {Shahid Beheshti University},
issn = {2345-5853},
eissn = {2345-5861},
doi = {},
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.},
keywords = {Idempotents,$\mathcal{R}$,$\mathcal{L}$,restriction semigroups,Zappa-Sz$\acute{\rm e}$p products},
url = {https://cgasa.sbu.ac.ir/article_4265.html},
eprint = {https://cgasa.sbu.ac.ir/article_4265_12a60e203d8dba10858f7e6a02feadc2.pdf}
}
@article {
author = {He, Wei},
title = {A note on semi-regular locales},
journal = {Categories and General Algebraic Structures with Applications},
volume = {1},
number = {1},
pages = {91-101},
year = {2013},
publisher = {Shahid Beheshti University},
issn = {2345-5853},
eissn = {2345-5861},
doi = {},
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.},
keywords = {locale,semi-regular locale,semi-regularization},
url = {https://cgasa.sbu.ac.ir/article_4266.html},
eprint = {https://cgasa.sbu.ac.ir/article_4266_cea1998c803fdf3e9a23488d516a8534.pdf}
}
@article {
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},
volume = {1},
number = {1},
pages = {103-117},
year = {2013},
publisher = {Shahid Beheshti University},
issn = {2345-5853},
eissn = {2345-5861},
doi = {},
abstract = {This work is devoted to give a charcaterization of a pomonoid $S$ such that all cyclic $S$-posets are regular injective.},
keywords = {Promonoid,Regular injectivity,Cyclic $S$-poset},
url = {https://cgasa.sbu.ac.ir/article_4267.html},
eprint = {https://cgasa.sbu.ac.ir/article_4267_6c49d6229329c34167027be1bc728633.pdf}
}
@article {
author = {},
title = {Persian Abstracts},
journal = {Categories and General Algebraic Structures with Applications},
volume = {1},
number = {1},
pages = {-},
year = {2013},
publisher = {Shahid Beheshti University},
issn = {2345-5853},
eissn = {2345-5861},
doi = {},
abstract = {},
keywords = {},
url = {https://cgasa.sbu.ac.ir/article_4829.html},
eprint = {https://cgasa.sbu.ac.ir/article_4829_4f1aa2c38aa118a25ddddddb53b8e144.pdf}
}