This study offers a revised classification of the movements involved in Teréza Nováková’s work, with specific reference to the novel Děti čistého živého (Children of Pure Living Spirit). Reference is made to the literary-historical and period metanarrative, emphasizing the presence of the ideal in the author’s work, which, however, was somewhat sidelined in the historical context, so that with the passage of time, Nováková was categorized under documentary realism. In the context of recent literary-history debates over the term ideal realism, and making use of the reception at that time, we demonstrate the stylization techniques Nováková used to construct, through her acknowledged work with oral and written documents, a text referring to the idea of nation-building based on culturally accepted paradigms.
In this paper, we introduce the concept of an ideal of a noncommutative dually residuated lattice ordered monoid and we show that congruence relations and certain ideals are in a one-to-one correspondence.
Dually residuated lattice ordered monoids (DRl-monoids) are common generalizations of, e.g., lattice ordered groups, Brouwerian algebras and algebras of logics behind fuzzy reasonings (MV -algebras, BL-algebras) and their non-commutative variants (GMV - algebras, pseudo BL-algebras). In the paper, lex-extensions and lex-ideals of DRl-monoids (which need not be commutative or bounded) satisfying a certain natural condition are studied.
Some results concerning congruence relations on partially ordered quasigroups (especially, Riesz quasigroups) and ideals of partially ordered loops are presented. These results generalize the assertions which were proved by Fuchs in [5] for partially ordered groups and Riesz groups.
In the present paper we introduce the notion of an ideal of a partial monounary algebra. Further, for an ideal $(I,f_I)$ of a partial monounary algebra $(A,f_A)$ we define the quotient partial monounary algebra $(A,f_A)/(I,f_I)$. Let $(X,f_X)$, $(Y,f_Y)$ be partial monounary algebras. We describe all partial monounary algebras $(P,f_P)$ such that $(X,f_X)$ is an ideal of $(P,f_P)$ and $(P,f_P)/(X,f_X)$ is isomorphic to $(Y,f_Y)$.
In this paper, we introduce a new class of residuated lattices called De Morgan residuated lattices, we show that the variety of De Morgan residuated lattices includes important subvarieties of residuated lattices such as Boolean algebras, MV-algebras, BL-algebras, Stonean residuated lattices, MTL-algebras and involution residuated lattices. We investigate specific properties of ideals in De Morgan residuated lattices, we state the prime ideal theorem and the pseudo-complementedness of the ideal lattice, we pay attention to prime, maximal, ⊙-prime ideals and to ideals that are meet-irreducible or meet-prime in the lattice of all ideals. We introduce the concept of an annihilator of a given subset of a De Morgan residuated lattice and we prove that annihilators are a particular kind of ideals. Also, regular annihilator and relative annihilator ideals are considered.
In the paper the notion of an ideal of a lattice ordered monoid A is introduced and relations between ideals of A and congruence relations on A are investigated. Further, it is shown that the set of all ideals of a soft lattice ordered monoid or a negatively ordered monoid partially ordered by inclusion is an algebraic Brouwerian lattice.
Order complex is an important object associated to a partially ordered set. Following a suggestion from V. A. Vassiliev (1994), we investigate an order complex associated to the partially ordered set of nontrivial ideals in a commutative ring with identity. We determine the homotopy type of the geometric realization for the order complex associated to a general commutative ring with identity. We show that this complex is contractible except for semilocal rings with trivial Jacobson radical when it is homotopy equivalent to a sphere., Nela Milošević, Zoran Z. Petrović., and Obsahuje seznam literatury
The article aims to compare the models of human subjectivity developed by Marek Siemek (in his post-Marxist period) and Evald Ilyenkov. Both authors define human subjectivity as a self-reflective relation between the “I” and the self. This self-referentiality is possible only in relation to the other, mediated through a non-subjective element. Subjectivity, therefore, is something essentially intersubjective for both philosophers. But even though these two perspectives share the same basic scheme, they are developed in very different ways. As I argue, the main difference between them can be seen in the conceptualisation of the third, objective element. Whereas Ilyenkov describes this element as a thing involved in human activity (for example, a tool) and therefore meaningful (a view strongly connected with his theory of the ideal), Siemek emphasises the role of the civil society and its institutions. Exploring this difference is especially important as it reflects an inherent political dimension in Ilyenkov’s and Siemek’s thought. I evaluate this political dimension, pointing to the originality of Siemek’s defence of capitalism and the Schillerian traces in both concepts.