On Islamic religious life and Islamic ethics in view of various Islamic stories.

We study classes of modules closed under direct sums, [Formula: see text]-submodules and [Formula: see text]-epimorphic images where [Formula: see text] is either the class of embeddings, RD-embeddings or pure embeddings. We show that the [Formula: see text]-injective modules of theses classes satisfy a Baer-like criterion. In particular, injective modules, RD-injective modules, pure injective modules, flat cotorsion modules and [Formula: see text]-torsion pure injective modules satisfy this criterion. The argument presented is a model theoretic one. We use in an essential (...) way stable independence relations which generalize Shelah’s non-forking to abstract elementary classes. We show that the classical model theoretic notion of superstability is equivalent to the algebraic notion of a noetherian category for these classes. We use this equivalence to characterize noetherian rings, pure semisimple rings, perfect rings and finite products of finite rings and artinian valuation rings via superstability. (shrink)

Journal of Mathematical Logic, Ahead of Print. We study classes of modules closed under direct sums, [math]-submodules and [math]-epimorphic images where [math] is either the class of embeddings, RD-embeddings or pure embeddings. We show that the [math]-injective modules of theses classes satisfy a Baer-like criterion. In particular, injective modules, RD-injective modules, pure injective modules, flat cotorsion modules and [math]-torsion pure injective modules satisfy this criterion. The argument presented is a model theoretic one. We use in an essential way stable independence (...) relations which generalize Shelah’s non-forking to abstract elementary classes. We show that the classical model theoretic notion of superstability is equivalent to the algebraic notion of a noetherian category for these classes. We use this equivalence to characterize noetherian rings, pure semisimple rings, perfect rings and finite products of finite rings and artinian valuation rings via superstability. (shrink)

Fisher [10] and Baur [6] showed independently in the seventies that if T is a complete first-order theory extending the theory of modules, then the class of models of T with pure embeddings is stable. In [25, 2.12], it is asked if the same is true for any abstract elementary class $(K, \leq _p)$ such that K is a class of modules and $\leq _p$ is the pure submodule relation. In this paper we give some instances where this is true:Theorem.Assume (...) R is an associative ring with unity. Let $(K, \leq _p)$ be an AEC such that $K \subseteq R\text {-Mod}$ and K is closed under finite direct sums, then: •If K is closed under pure-injective envelopes, then $\mathbf {K}$ is $\lambda $ -stable for every $\lambda \geq \operatorname {LS}(\mathbf {K})$ such that $\lambda ^{|R| + \aleph _0}= \lambda $.•If K is closed under pure submodules and pure epimorphic images, then $\mathbf {K}$ is $\lambda $ -stable for every $\lambda $ such that $\lambda ^{|R| + \aleph _0}= \lambda $.•Assume R is Von Neumann regular. If $\mathbf {K}$ is closed under submodules and has arbitrarily large models, then $\mathbf {K}$ is $\lambda $ -stable for every $\lambda $ such that $\lambda ^{|R| + \aleph _0}= \lambda $.As an application of these results we give new characterizations of noetherian rings, pure-semisimple rings, Dedekind domains, and fields via superstability. Moreover, we show how these results can be used to show a link between being good in the stability hierarchy and being good in the axiomatizability hierarchy.Another application is the existence of universal models with respect to pure embeddings in several classes of modules. Among them, the class of flat modules and the class of $\mathfrak {s}$ -torsion modules. (shrink)

We show that certain classes of modules have universal models with respect to pure embeddings: Let R be a ring, T a first‐order theory with an infinite model extending the theory of R‐modules and (where ⩽pp stands for “pure submodule”). Assume has the joint embedding and amalgamation properties. If or, then has a universal model of cardinality λ. As a special case, we get a recent result of Shelah [28, 1.2] concerning the existence of universal reduced torsion‐free abelian groups with (...) respect to pure embeddings.We begin the study of limit models for classes of R‐modules with joint embedding and amalgamation. We show that limit models with chains of long cofinality are pure‐injective and we characterize limit models with chains of countable cofinality. This can be used to answer [18, Question 4.25].As this paper is aimed at model theorists and algebraists an effort was made to provide the background for both. (shrink)

We introduce the notion of a w-good \-frame which is a weakening of Shelah’s notion of a good \-frame. Existence of a w-good \-frame implies existence of a model of size \. Tameness and amalgamation imply extension of a w-good \-frame to larger models. As an application we show:Theorem 0.1. Suppose\. If \ = \mathbb {I} = 1 \le \mathbb {I} < 2^{\lambda ^{++}}\)and\is\\)-tame, then\.The proof presented clarifies some of the details of the main theorem of Shelah and avoids using (...) the heavy set-theoretic machinery of Shelah by replacing it with tameness. (shrink)

There are many results in the literature where superstablity-like independence notions, without any categoricity assumptions, have been used to show the existence of larger models. In this paper we show that stability is enough to construct larger models for small cardinals assuming a mild locality condition for Galois types. Theorem 0.1. Suppose $\lambda <2^{\aleph _0}$. Let ${\mathbf {K}}$ be an abstract elementary class with $\lambda \geq {\operatorname {LS}}({\mathbf {K}})$. Assume ${\mathbf {K}}$ has amalgamation in $\lambda $, no maximal model in (...) $\lambda $, and is stable in $\lambda $. If ${\mathbf {K}}$ is $(<\lambda ^+, \lambda )$ -local, then ${\mathbf {K}}$ has a model of cardinality $\lambda ^{++}$. The set theoretic assumption that $\lambda <2^{\aleph _0}$ and model theoretic assumption of stability in $\lambda $ can be weakened to the model theoretic assumptions that $|{\mathbf {S}}^{na}(M)|< 2^{\aleph _0}$ for every $M \in {\mathbf {K}}_\lambda $ and stability for $\lambda $ -algebraic types in $\lambda $. This is a significant improvement of Theorem 0.1, as the result holds on some unstable abstract elementary classes. (shrink)

We study Martsinkovsky–Russell torsion modules with pure embeddings as an abstract elementary class. We give a model-theoretic characterization of the pure-injective and the Σ-pure-injective modules relative to the class of torsion modules assuming that the torsion submodule is a pure submodule. Our characterization of relative Σ-pure-injective modules extends the classical characterization of Gruson and Jenson as well as Zimmermann. We study the limit models of the class and determine when the class is superstable assuming that the torsion submodule is a (...) pure submodule. As a corollary, we show that the class of torsion abelian groups with pure embeddings is strictly stable (i.e., stable not superstable). (shrink)

Articles on moral and ethics according to Islamic teachings.

Islamic ethics - Early works to 20th century.

From classic aesthetic theories to fresh aesthetic methods, this volume is an accessible introduction to the main topics in contemporary aesthetics: the media-technological challenges, transcultural aesthetics and aesthetic methodology.

jild-i 1. al-Taṣawwurāt -- jild-i 2. al-Taṣdīqāt.

Wydaje się, że filozofia rzadko miała związek z muzyką - Rousseau, Nietzsche czy Adorno to wyjątki. A jednak w mitologii i tradycji greckiej związki takie były bardzo wyraźne: koźlonogi Pan, który zdradził Apollinowi tajemnicę wieszczenia, był muzycznym wirtuozem; ucieleśniający mądrość Sylen uczył Dionizosa śpiewu i tańca; Apollo, stanąwszy na czele korowodu szalonych muz, uczynił je przewodniczkami poetów; sami zaś poeci posiadali umiejętność rozumienia ludzkiej natury oraz dar przepowiadania przyszłości i uosabiali natchnioną mądrość. Przynajmniej więc w pewnym stopniu filozofia wywodzi się (...) z muzyki. Koneksje te zaś potwierdza osoba Gilles’a Deleuze’a, którego nomadologia oraz takie kategorie, jak „kłącze”, „refren”, „powtórzenie” czy „deterytorializacja”, stały się istotnymi wyznacznikami dla współczesnej eksperymentalnej muzyki elektronicznej. (shrink)

jild-i 1. Az zamān-i bāstān tā māʼah-i hafdahum, muz̲ayyal bi-tarjamah-ʼi guftār-i Dikārt faylasūf-i nāmī-i Farānsavī -- jild-i 3. Az āghāz-i sadah-i nūzdahum tā zamān-i ḥāz̤ir).

As a leading scientist of the 13th century C. E. Quṭb al-Dīn Shīrāzī wrote three substantial works on hay'a (or the configuration of the celestial orbs): Nihāyat al-idrāk fī dirāyat al-aflāk ("The Limits of Attainment in the Understanding of the Heavens"), al-Tuḥfa al-shāhīya fī 'ilm al-hay'a ("The Royal Offering Regarding the Knowledge of the Configuration of the Heavens"), and Ikhtīyārāt-i Muẓaffarī ("The Muẓaffarī Elections"). Completed in less than four years and written in two of the classical languages of the Islamic (...) world, Arabic and Persian, these works provide a fascinating window to the astronomical research carried out in Ilkhanid Persia. Shīrāzī and his colleagues were driven by their desire to rid Ptolemaic astronomy from its perceived shortcomings. An intriguing trail of revisions and emendations in Shīrāzī's hay'a texts serves to highlight both those features of Shīrāzī's astronomy that were inherited from his predecessors, as well as his original contributions to this branch of astronomical research. As a renowned savant, Shīrāzī spent a large portion of his career near centers of political power in Persia and Anatolia. A study of his scientific output and career as a scholar is an opportunity, therefore, for an examination of the patronage of science and of scientific works within the Ilkhanid realms. Not only was this patronage important to the work of scholars such as Shīrāzī but it was critical to the founding and operation of one of the foremost scientific institutions of the medieval Islamic world, the Marāgha observatory. The astronomical tradition in which Shīrāzī carried out his research has many links, as well, to the astronomy of Early Modern Europe, as can be seen in the astronomical models of Copernicus. (shrink)