1 - 6 of 6
Number of results to display per page
Search Results
2. Annihilators in BCK-algebras
- Creator:
- Halaš, Radomír
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- BCK-algebra, deductive system, annihilator, and pseudocomplement
- Language:
- English
- Description:
- We introduce the concepts of an annihilator and a relative annihilator of a given subset of a BCK-algebra $\mathcal A$. We prove that annihilators of deductive systems of BCK-algebras are again deductive systems and moreover pseudocomplements in the lattice $\mathcal D (A)$ of all deductive systems on $\mathcal A$. Moreover, relative annihilators of $C\in \mathcal D (A)$ with respect to $B \in \mathcal D (A)$ are introduced and serve as relative pseudocomplements of $C$ w.r.t. $B$ in $\mathcal D (A)$.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
3. Annihilators in normal autometrized algebras
- Creator:
- Chajda, Ivan and Rachůnek, Jiří
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- autometrized algebra, annihilator, relative annihilator, ideal, and polar
- Language:
- English
- Description:
- The concepts of an annihilator and a relative annihilator in an autometrized $l$-algebra are introduced. It is shown that every relative annihilator in a normal autometrized $l$-algebra $\mathcal {A}$ is an ideal of $\mathcal {A}$ and every principal ideal of $\mathcal {A}$ is an annihilator of $\mathcal {A}$. The set of all annihilators of $\mathcal {A}$ forms a complete lattice. The concept of an $I$-polar is introduced for every ideal $I$ of $\mathcal {A}$. The set of all $I$-polars is a complete lattice which becomes a two-element chain provided $I$ is prime. The $I$-polars are characterized as pseudocomplements in the lattice of all ideals of $\mathcal {A}$ containing $I$.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
4. On ideals in De Morgen residuated lattices
- Creator:
- Holdon, Liviu-Constantin
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- residuated lattice, De Morgan laws, filter, deductive system, ideal, ∩-prime, ∩-irreducible, and annihilator
- Language:
- English
- Description:
- 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.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
5. 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
6. Skew inverse power series rings over a ring with projective socle
- Creator:
- Paykan, Kamal
- Format:
- print, bez média, and svazek
- Type:
- model:article and TEXT
- Subject:
- mathematics, flat socle ring, skew inverse power series ring, skew polynomial ring, annihilator, projective socle ring, 13, and 51
- Language:
- English
- Description:
- A ring R is called a right PS-ring if its socle, Soc(RR), is projective. Nicholson and Watters have shown that if R is a right PS-ring, then so are the polynomial ring R[x] and power series ring R[[x]]. In this paper, it is proved that, under suitable conditions, if R has a (flat) projective socle, then so does the skew inverse power series ring R[[x−1; alfa, delta]] and the skew polynomial ring R[x; alfa, delta], where R is an associative ring equipped with an automorphism and an alfa-derivation delta. Our results extend and unify many existing results. Examples to illustrate and delimit the theory are provided., Kamal Paykan., and Seznam literatury
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public