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21. Principal ideals of finitely generated commutative monoids

Creator:
Rosales, José Carlos and García-García, Juan Ignacio
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
monoid, ideal, cancellative, and torsion free
Language:
English
Description:
We study the semigroups isomorphic to principal ideals of finitely generated commutative monoids. We define the concept of finite presentation for this kind of semigroups. Furthermore, we show how to obtain information on these semigroups from their presentations.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

22. Relative polars in ordered sets

Creator:
Halaš, Radomír
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
ordered set, distributive set, ideal, prime ideal, $R$-polar, and annihilator
Language:
English
Description:
In the paper, the notion of relative polarity in ordered sets is introduced and the lattices of $R$-polars are studied. Connections between $R$-polars and prime ideals, especially in distributive sets, are found.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

23. Some generalizations of Olivier's theorem

Creator:
Faisant, Alain, Grekos, Georges, and Mišík, Ladislav
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
convergent series, Olivier’s theorem, ideal, I-convergence, and I-monotonicity
Language:
English
Description:
Let ∑ ∞ n=1 an be a convergent series of positive real numbers. L. Olivier proved that if the sequence (an) is non-increasing, then lim n→∞ nan = 0. In the present paper: (a) We formulate and prove a necessary and sufficient condition for having lim n→∞ nan = 0; Olivier’s theorem is a consequence of our Theorem 2.1. (b) We prove properties analogous to Olivier’s property when the usual convergence is replaced by the I-convergence, that is a convergence according to an ideal I of subsets of ℕ. Again, Olivier’s theorem is a consequence of our Theorem 3.1, when one takes as I the ideal of all finite subsets of ℕ.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

24. Subalgebra extensions of partial monounary algebras

Creator:
Jakubíková-Studenovská, Danica
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
partial monounary algebra, subalgebra, congruence, quotient algebra, subalgebra extension, ideal, and ideal extension
Language:
English
Description:
For a subalgebra ${\mathcal B}$ of a partial monounary algebra ${\mathcal A}$ we define the quotient partial monounary algebra ${\mathcal A}/{\mathcal B}$. Let ${\mathcal B}$, ${\mathcal C}$ be partial monounary algebras. In this paper we give a construction of all partial monounary algebras ${\mathcal A}$ such that ${\mathcal B}$ is a subalgebra of ${\mathcal A}$ and ${\mathcal C}\cong {\mathcal A}/{\mathcal B}$.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

25. Two ideals connected with strong right upper porosity at a point

Creator:
Bilet, Viktoriia, Dovgoshey, Oleksiy, and Prestin, Jürgen
Format:
print, bez média, and svazek
Type:
model:article and TEXT
Subject:
matematika, mathematics, one-side porosity, local strong upper porosity, completely strongly porous set, ideal, 13, and 51
Language:
English
Description:
Let SP be the set of upper strongly porous at 0 subsets of \mathbb{R}^{+} and let Î(SP) be the intersection of maximal ideals I\subseteq SP. Some characteristic properties of sets E \in Î(SP) are obtained. We also find a characteristic property of the intersection of all maximal ideals contained in a given set which is closed under subsets. It is shown that the ideal generated by the so-called completely strongly porous at 0 subsets of \mathbb{R}^{+} is a proper subideal of Î(SP). Earlier, completely strongly porous sets and some of their properties were studied in the paper V.Bilet, O.Dovgoshey (2013/2014)., Viktoriia Bilet, Oleksiy Dovgoshey, Jürgen Prestin., and Obsahuje seznam literatury
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

26. α-ideals in 0-distributive posets

Creator:
Mokbel, Khalid A
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
0-distributive poset, ideal, α-ideal, prime ideal, non-dense ideal, minimal ideal, and annihilator ideal
Language:
English
Description:
The concept of α-ideals in posets is introduced. Several properties of α-ideals in 0-distributive posets are studied. Characterization of prime ideals to be α-ideals in 0- distributive posets is obtained in terms of minimality of ideals. Further, it is proved that if a prime ideal I of a 0-distributive poset is non-dense, then I is an α-ideal. Moreover, it is shown that the set of all α-ideals α Id(P) of a poset P with 0 forms a complete lattice. A result analogous to separation theorem for finite 0-distributive posets is obtained with respect to prime α-ideals. Some counterexamples are also given.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public