Abstract Let be a commutative ring with identity and 𝒜() be the set of ideals with non-zero annihilator. The strongly annihilating-ideal graph of is defined as the graph SAG() with the vertex set 𝒜 ()* = 𝒜 () {0} and two distinct vertices I and J are adjacent if and only if I ∩ Ann(J) ≠ (0) and J ∩ Ann(I) ≠ (0). In this paper, we study the metric dimension of SAG() and some metric dimension formulae for strongly annihilating-ideal graphs are given.
{"title":"On the metric dimension of strongly annihilating-ideal graphs of commutative rings","authors":"V. Soleymanivarniab, R. Nikandish, A. Tehranian","doi":"10.2478/ausm-2020-0025","DOIUrl":"https://doi.org/10.2478/ausm-2020-0025","url":null,"abstract":"Abstract Let be a commutative ring with identity and 𝒜() be the set of ideals with non-zero annihilator. The strongly annihilating-ideal graph of is defined as the graph SAG() with the vertex set 𝒜 ()* = 𝒜 () {0} and two distinct vertices I and J are adjacent if and only if I ∩ Ann(J) ≠ (0) and J ∩ Ann(I) ≠ (0). In this paper, we study the metric dimension of SAG() and some metric dimension formulae for strongly annihilating-ideal graphs are given.","PeriodicalId":43054,"journal":{"name":"Acta Universitatis Sapientiae-Mathematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2020-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81043733","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract In this paper we introduce the new types of separation axioms called λD − R0 and λD − R1 spaces, by using λD-open set. The notion λD − R0 and λD − R1 spaces are introduced and some of their properties are investigated.
{"title":"On λD − R0 and λD − R1 spaces","authors":"Sarhad F. Namiq, E. Rosas","doi":"10.2478/ausm-2020-0022","DOIUrl":"https://doi.org/10.2478/ausm-2020-0022","url":null,"abstract":"Abstract In this paper we introduce the new types of separation axioms called λD − R0 and λD − R1 spaces, by using λD-open set. The notion λD − R0 and λD − R1 spaces are introduced and some of their properties are investigated.","PeriodicalId":43054,"journal":{"name":"Acta Universitatis Sapientiae-Mathematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2020-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81311254","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
M. Shahraki, S. Sedghi, S. Aleomraninejad, Z. Mitrović
Abstract In this paper, a general form of the Suzuki type function is considered on S- metric space, to get a fixed point. Then we show that our results generalize some old results.
{"title":"Some fixed point results on S-metric spaces","authors":"M. Shahraki, S. Sedghi, S. Aleomraninejad, Z. Mitrović","doi":"10.2478/ausm-2020-0024","DOIUrl":"https://doi.org/10.2478/ausm-2020-0024","url":null,"abstract":"Abstract In this paper, a general form of the Suzuki type function is considered on S- metric space, to get a fixed point. Then we show that our results generalize some old results.","PeriodicalId":43054,"journal":{"name":"Acta Universitatis Sapientiae-Mathematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2020-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85177932","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract In this work, soft covered ideals in semigroups are constructed and in this concept, soft covered semigroups, soft covered left (right) ideals, soft covered interior ideals, soft covered (generalized) bi-ideals and soft covered quasi ideals of a semigroup are defined. Various properties of these ideals are introduced and the interrelations of these soft covered ideals and the relations of soft anti covered ideals and soft covered ideals are investigated.
{"title":"Soft covered ideals in semigroups","authors":"Şerif Özlü, A. Sezgi̇n","doi":"10.2478/ausm-2020-0023","DOIUrl":"https://doi.org/10.2478/ausm-2020-0023","url":null,"abstract":"Abstract In this work, soft covered ideals in semigroups are constructed and in this concept, soft covered semigroups, soft covered left (right) ideals, soft covered interior ideals, soft covered (generalized) bi-ideals and soft covered quasi ideals of a semigroup are defined. Various properties of these ideals are introduced and the interrelations of these soft covered ideals and the relations of soft anti covered ideals and soft covered ideals are investigated.","PeriodicalId":43054,"journal":{"name":"Acta Universitatis Sapientiae-Mathematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2020-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72417022","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract Let k be an arbitrary field and Q a tame quiver of type ˜D4. Consider the path algebra kQ and the category of finite dimensional right modules mod-kQ. We determine the Hall polynomials Fxyz associated to indecomposable modules of defect ∂z =−2, ∂x = ∂y =−1 or dually ∂z = 2, ∂x = ∂y = 1.
{"title":"On some Hall polynomials over a quiver of type ˜D4","authors":"Csaba Szántó, I. Szöllősi","doi":"10.2478/ausm-2020-0028","DOIUrl":"https://doi.org/10.2478/ausm-2020-0028","url":null,"abstract":"Abstract Let k be an arbitrary field and Q a tame quiver of type ˜D4. Consider the path algebra kQ and the category of finite dimensional right modules mod-kQ. We determine the Hall polynomials Fxyz associated to indecomposable modules of defect ∂z =−2, ∂x = ∂y =−1 or dually ∂z = 2, ∂x = ∂y = 1.","PeriodicalId":43054,"journal":{"name":"Acta Universitatis Sapientiae-Mathematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2020-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80238249","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract New sufficient conditions involving the properties of analytic functions to belong to the class of Carathéodory functions are investigated. Certain univalence and starlikeness conditions are deduced as special cases of main results.
{"title":"On application of differential subordination for Carathéodory functions","authors":"V. Lavanya, M. P. Jeyaraman, H. A. Farzana","doi":"10.2478/ausm-2020-0026","DOIUrl":"https://doi.org/10.2478/ausm-2020-0026","url":null,"abstract":"Abstract New sufficient conditions involving the properties of analytic functions to belong to the class of Carathéodory functions are investigated. Certain univalence and starlikeness conditions are deduced as special cases of main results.","PeriodicalId":43054,"journal":{"name":"Acta Universitatis Sapientiae-Mathematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2020-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84304539","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract A signed graph Σ is a graph with positive or negative signs attatched to each of its edges. A signed graph Σ is balanced if each of its cycles has an even number of negative edges. Restrained dominating set D in Σ is a restrained dominating set of its underlying graph where the subgraph induced by the edges across Σ[D : V D] and within V D is balanced. The set D having least cardinality is called minimum restrained dominating set and its cardinality is the restrained domination number of Σ denoted by γr(Σ). The ability to communicate rapidly within the network is an important application of domination in social networks. The main aim of this paper is to initiate a study on restrained domination in the realm of different classes of signed graphs.
带符号图Σ是指每条边都带有正号或负号的图。如果一个有符号图Σ的每个循环都有偶数条负边，那么它就是平衡的。Σ中的约束支配集D是其底层图的约束支配集，其中穿过Σ[D: V D]和在V D内的边所诱导的子图是平衡的。具有最小基数的集合D称为最小约束支配集，其基数为Σ的约束支配数，用γr(Σ)表示。在社交网络中，快速沟通的能力是支配地位的重要应用。本文的主要目的是研究不同类别的符号图领域中的约束支配问题。
{"title":"Restrained domination in signed graphs","authors":"A. J. Mathias, V. Sangeetha, M. Acharya","doi":"10.2478/ausm-2020-0010","DOIUrl":"https://doi.org/10.2478/ausm-2020-0010","url":null,"abstract":"Abstract A signed graph Σ is a graph with positive or negative signs attatched to each of its edges. A signed graph Σ is balanced if each of its cycles has an even number of negative edges. Restrained dominating set D in Σ is a restrained dominating set of its underlying graph where the subgraph induced by the edges across Σ[D : V D] and within V D is balanced. The set D having least cardinality is called minimum restrained dominating set and its cardinality is the restrained domination number of Σ denoted by γr(Σ). The ability to communicate rapidly within the network is an important application of domination in social networks. The main aim of this paper is to initiate a study on restrained domination in the realm of different classes of signed graphs.","PeriodicalId":43054,"journal":{"name":"Acta Universitatis Sapientiae-Mathematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2020-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80236218","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract In this paper a new class of sets termed as ω∗μ-open sets has been introduced and studied. Using these concept, a unified theory for decomposition of (μ, λ)-continuity has been given.
{"title":"More on decomposition of generalized continuity","authors":"B. Roy","doi":"10.2478/ausm-2020-0014","DOIUrl":"https://doi.org/10.2478/ausm-2020-0014","url":null,"abstract":"Abstract In this paper a new class of sets termed as ω∗μ-open sets has been introduced and studied. Using these concept, a unified theory for decomposition of (μ, λ)-continuity has been given.","PeriodicalId":43054,"journal":{"name":"Acta Universitatis Sapientiae-Mathematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2020-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83093667","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract Collatz conjecture states that iterating the map that takes even natural number n to n2 {n over 2} and odd natural number n to 3n + 1, will eventually obtain 1. In this paper a new generalization of the Collatz conjecture is analyzed and some interesting results are obtained. Since Collatz conjecture can be seen as a particular case of the generalization introduced in this articule, several more general conjectures are also presented.
{"title":"Collatz conjecture revisited: an elementary generalization","authors":"Amauri Gutiérrez","doi":"10.2478/ausm-2020-0007","DOIUrl":"https://doi.org/10.2478/ausm-2020-0007","url":null,"abstract":"Abstract Collatz conjecture states that iterating the map that takes even natural number n to n2 {n over 2} and odd natural number n to 3n + 1, will eventually obtain 1. In this paper a new generalization of the Collatz conjecture is analyzed and some interesting results are obtained. Since Collatz conjecture can be seen as a particular case of the generalization introduced in this articule, several more general conjectures are also presented.","PeriodicalId":43054,"journal":{"name":"Acta Universitatis Sapientiae-Mathematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2020-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84166426","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract Let R be a Noetherian integral domain which is also an algebra over ℚ (ℚ is the field of rational numbers). Let σ be an endo-morphism of R and δ a σ-derivation of R. We recall that a ring R is a weak (σ, δ)-rigid ring if a(σ(a)+ δ(a)) ∈ N(R) if and only if a ∈ N(R) for a ∈ R (N(R) is the set of nilpotent elements of R). With this we prove that if R is a Noetherian integral domain which is also an algebra over ℚ, σ an automorphism of R and δ a σ-derivation of R such that R is a weak (σ, δ)-rigid ring, then N(R) is completely semiprime.
{"title":"On weak (σ, δ)-rigid rings over Noetherian rings","authors":"V. K. Bhat, P. Singh, S. Sharma","doi":"10.2478/ausm-2020-0001","DOIUrl":"https://doi.org/10.2478/ausm-2020-0001","url":null,"abstract":"Abstract Let R be a Noetherian integral domain which is also an algebra over ℚ (ℚ is the field of rational numbers). Let σ be an endo-morphism of R and δ a σ-derivation of R. We recall that a ring R is a weak (σ, δ)-rigid ring if a(σ(a)+ δ(a)) ∈ N(R) if and only if a ∈ N(R) for a ∈ R (N(R) is the set of nilpotent elements of R). With this we prove that if R is a Noetherian integral domain which is also an algebra over ℚ, σ an automorphism of R and δ a σ-derivation of R such that R is a weak (σ, δ)-rigid ring, then N(R) is completely semiprime.","PeriodicalId":43054,"journal":{"name":"Acta Universitatis Sapientiae-Mathematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2020-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73944111","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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