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Discussiones Mathematicae - General Algebra and Applications最新文献

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On Partial Clones of K-Terms 关于k项的部分克隆
Discussiones Mathematicae - General Algebra and Applications Pub Date : 2021-09-06 DOI: 10.7151/dmgaa.1376
N. Lekkoksung, S. Lekkoksung
{"title":"On Partial Clones of K-Terms","authors":"N. Lekkoksung, S. Lekkoksung","doi":"10.7151/dmgaa.1376","DOIUrl":"https://doi.org/10.7151/dmgaa.1376","url":null,"abstract":"Abstract The main purpose of this paper is to generalize the concept of linear terms. A linear term is a term in which every variable occurs at most once. K. Denecke defined partial operations on linear terms and partial clones. Moreover, their properties are also studied. In the present paper, a generalized notion of the partial clone of linear terms, which is called k-terms clone, is presented and we also study its properties. We provide a characterization of the k-terms clone being free with respect to itself. Moreover, we attempt to define mappings analogue to the concept of hypersubstitutions.","PeriodicalId":36816,"journal":{"name":"Discussiones Mathematicae - General Algebra and Applications","volume":"41 1","pages":"361 - 379"},"PeriodicalIF":0.0,"publicationDate":"2021-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71123195","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}
引用次数: 2
Revisiting Faigle geometries from a perspective of semimodular lattices 从半模格的角度重新审视费格尔几何
Discussiones Mathematicae - General Algebra and Applications Pub Date : 2021-07-21 DOI: 10.7151/dmgaa.1416
G'abor Cz'edli
{"title":"Revisiting Faigle geometries from a perspective of semimodular lattices","authors":"G'abor Cz'edli","doi":"10.7151/dmgaa.1416","DOIUrl":"https://doi.org/10.7151/dmgaa.1416","url":null,"abstract":"In 1980, U. Faigle introduced a sort of finite geometries on posets that are in bijective correspondence with finite semimodular lattices. His result has almost been forgotten in lattice theory. Here we simplify the axiomatization of these geometries, which we call Faigle geometries. To exemplify their usefulness, we give a short proof of a theorem of Grätzer and E. Knapp (2009) asserting that each slim semimodular lattice L has a congruence-preserving extension to a slim rectangular lattice of the same length as L. As another application of Faigle geometries, we give a short proof of G. Grätzer and E. W. Kiss’ result from 1986 (also proved by M. Wild in 1993, the present author and E. T. Schmidt in 2010, and B. Skublics in 2013) that each finite semimodular lattice L has an extension to a geometric lattice of the same length as L.","PeriodicalId":36816,"journal":{"name":"Discussiones Mathematicae - General Algebra and Applications","volume":"14 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41286310","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}
引用次数: 4
Revisiting the Representation Theorem of Finite Distributive Lattices with Principal Congruences. A Proof-By-Picture Approach 重述具有主同余的有限分配格的表示定理。图片证明方法
Discussiones Mathematicae - General Algebra and Applications Pub Date : 2021-04-28 DOI: 10.7151/dmgaa.1375
G. Grätzer, H. Lakser
{"title":"Revisiting the Representation Theorem of Finite Distributive Lattices with Principal Congruences. A Proof-By-Picture Approach","authors":"G. Grätzer, H. Lakser","doi":"10.7151/dmgaa.1375","DOIUrl":"https://doi.org/10.7151/dmgaa.1375","url":null,"abstract":"Abstract A classical result of R.P. Dilworth states that every finite distributive lattice D can be represented as the congruence lattice of a finite lattice L. A sharper form was published in G. Grätzer and E.T. Schmidt in 1962, adding the requirement that all congruences in L be principal. Another variant, published in 1998 by the authors and E.T. Schmidt, constructs a planar semimodular lattice L. In this paper, we merge these two results: we construct L as a planar semimodular lattice in which all congruences are principal. This paper relies on the techniques developed by the authors and E.T. Schmidt in the 1998 paper.","PeriodicalId":36816,"journal":{"name":"Discussiones Mathematicae - General Algebra and Applications","volume":"41 1","pages":"411 - 417"},"PeriodicalIF":0.0,"publicationDate":"2021-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47754899","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}
引用次数: 0
All Maximal Idempotent Submonoids of Generalized Cohypersubstitutions of Type τ = (2) τ=（2）型广义上超置换的所有极大幂等子模
Discussiones Mathematicae - General Algebra and Applications Pub Date : 2021-04-06 DOI: 10.7151/dmgaa.1351
Nagornchat Chansuriya
{"title":"All Maximal Idempotent Submonoids of Generalized Cohypersubstitutions of Type τ = (2)","authors":"Nagornchat Chansuriya","doi":"10.7151/dmgaa.1351","DOIUrl":"https://doi.org/10.7151/dmgaa.1351","url":null,"abstract":"Abstract A generalized cohypersubstitution of type τ is a mapping σ which maps every ni-ary cooperation symbol fi to the coterm σ(f ) of type τ = (ni)i∈I. Denote by CohypG(τ) the set of all generalized cohypersubstitutions of type τ. Define the binary operation ◦CG on CohypG(τ) by σ1◦CG σ2:= σ ˆ1 ◦ σ2 for all σ1, σ2 ∈ CohypG(τ) and σid(fi) := fi for all i ∈ I. Then CohypG(τ) := {CohypG(τ), ◦CG, σid} is a monoid. In [5], the monoid CohypG(2) was studied. They characterized and presented the idempotent and regular elements of this monoid. In this present paper, we consider the set of all idempotent elements of the monoid CohypG(2) and determine all maximal idempotent submonoids of this monoid.","PeriodicalId":36816,"journal":{"name":"Discussiones Mathematicae - General Algebra and Applications","volume":"41 1","pages":"45 - 54"},"PeriodicalIF":0.0,"publicationDate":"2021-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43079958","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}
引用次数: 0
Equivalent Forms for a Poset to Be Modular Poset 偏序集为模偏序集的等价形式
Discussiones Mathematicae - General Algebra and Applications Pub Date : 2021-04-06 DOI: 10.7151/dmgaa.1358
P. Sundarayya, T. R. Kishore
{"title":"Equivalent Forms for a Poset to Be Modular Poset","authors":"P. Sundarayya, T. R. Kishore","doi":"10.7151/dmgaa.1358","DOIUrl":"https://doi.org/10.7151/dmgaa.1358","url":null,"abstract":"Abstract The notion of modular and distributive posets which generalize the corresponding notions from the lattice theory are introduced by J. Larmerova and J. Rachnek. Later some extended results of uniquely complemented lattice are derived to uniquely complemented posets. Now, in this paper, some equivalent conditions for a poset to be modular poset are given.","PeriodicalId":36816,"journal":{"name":"Discussiones Mathematicae - General Algebra and Applications","volume":"41 1","pages":"5 - 13"},"PeriodicalIF":0.0,"publicationDate":"2021-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48734738","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}
引用次数: 0
From ∨e-Semigroups to Hypersemigroups 从对半群到超半群
Discussiones Mathematicae - General Algebra and Applications Pub Date : 2021-04-06 DOI: 10.7151/dmgaa.1353
N. Kehayopulu
{"title":"From ∨e-Semigroups to Hypersemigroups","authors":"N. Kehayopulu","doi":"10.7151/dmgaa.1353","DOIUrl":"https://doi.org/10.7151/dmgaa.1353","url":null,"abstract":"Abstract A poe-semigroup is a semigroup S at the same time an ordered set having a greatest element “e” in which the multiplication is compatible with the ordering. A ∨e-semigroup is a semigroup S at the same time an upper semilattice with a greatest element “e” such that a(b ∨ c) = ab ∨ ac and (a ∨ b)c = ac ∨ bc for every a, b, c ∈ S. If S is not only an upper semi-lattice but a lattice, then it is called le-semigroup. From many results on le-semigroups, ∨e-semigroups or poe-semigroups, corresponding results on ordered semigroups (without greatest element) can be obtained. Related results on hypersemigroups or ordered hypersemigroups follow as application. An example is presented in the present note; the same can be said for every result on these structures. So order-lattices play an essential role in studying the hypersemigroups and the ordered hypersemigroups.","PeriodicalId":36816,"journal":{"name":"Discussiones Mathematicae - General Algebra and Applications","volume":"41 1","pages":"113 - 126"},"PeriodicalIF":0.0,"publicationDate":"2021-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44776096","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}
引用次数: 2
Unitary Invertible Graphs of Finite Rings 有限环的酉可逆图
Discussiones Mathematicae - General Algebra and Applications Pub Date : 2021-04-06 DOI: 10.7151/dmgaa.1350
T. Chalapathi, Shaik Sajana
{"title":"Unitary Invertible Graphs of Finite Rings","authors":"T. Chalapathi, Shaik Sajana","doi":"10.7151/dmgaa.1350","DOIUrl":"https://doi.org/10.7151/dmgaa.1350","url":null,"abstract":"Abstract Let R be a finite commutative ring with unity. In this paper, we consider set of additive and mutual additive inverses of group units of R and obtain interrelations between them. In general φ(Zn) is even, however we demonstrate that φ(R) is odd for any finite commutative ring with unity of Char(R) ≠ 2. Further, we present unitary invertible graph related with self and mutual additive inverses of group units. At long last, we establish a formula for counting the total number of basic and non-basic triangles in the unitary invertible graph.","PeriodicalId":36816,"journal":{"name":"Discussiones Mathematicae - General Algebra and Applications","volume":"41 1","pages":"195 - 208"},"PeriodicalIF":0.0,"publicationDate":"2021-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46600836","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}
引用次数: 1
Tri-Quasi Ideals of Γ-Semirings Γ-半环的三拟理想
Discussiones Mathematicae - General Algebra and Applications Pub Date : 2021-04-06 DOI: 10.7151/dmgaa.1360
M. M. Rao
{"title":"Tri-Quasi Ideals of Γ-Semirings","authors":"M. M. Rao","doi":"10.7151/dmgaa.1360","DOIUrl":"https://doi.org/10.7151/dmgaa.1360","url":null,"abstract":"Abstract In this paper, as a further generalization of ideals, we introduce the notion of tri-quasi ideal as a generalization of ideal, left ideal, right ideal, bi-ideal, quasi ideal, interior ideal, bi-interior ideal,weak interior ideal, bi-quasi ideal, tri-ideal,quasi-interior ideal and bi-quasi-interior ideal of Γ-semiring. Some charecterizations of Γ-semiring,regular Γ-semiring and simple Γ-semiring using tri-quasi ideals are given and study the properties of tri-quasi ideals of Γ-semiring.","PeriodicalId":36816,"journal":{"name":"Discussiones Mathematicae - General Algebra and Applications","volume":"41 1","pages":"33 - 44"},"PeriodicalIF":0.0,"publicationDate":"2021-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46716839","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}
引用次数: 1
Applying the Czédli-Schmidt Sequences to Congruence Properties of Planar Semimodular Lattices cz<s:1> -施密特序列在平面半模格同余性质上的应用
Discussiones Mathematicae - General Algebra and Applications Pub Date : 2021-04-06 DOI: 10.7151/dmgaa.1359
G. Grätzer
{"title":"Applying the Czédli-Schmidt Sequences to Congruence Properties of Planar Semimodular Lattices","authors":"G. Grätzer","doi":"10.7151/dmgaa.1359","DOIUrl":"https://doi.org/10.7151/dmgaa.1359","url":null,"abstract":"Abstract Following Grätzer and Knapp, 2009, a planar semimodular lattice L is rectangular, if the left boundary chain has exactly one doubly-irreducible element, cl, and the right boundary chain has exactly one doubly-irreducible element, cr, and these elements are complementary. The Czédli-Schmidt Sequences, introduced in 2012, construct rectangular lattices. We use them to prove some structure theorems. In particular, we prove that for a slim (no M3 sublattice) rectangular lattice L, the congruence lattice Con L has exactly length[cl, 1] + length[cr, 1] dual atoms and a dual atom in Con L is a congruence with exactly two classes. We also describe the prime ideals in a slim rectangular lattice.","PeriodicalId":36816,"journal":{"name":"Discussiones Mathematicae - General Algebra and Applications","volume":"41 1","pages":"153 - 169"},"PeriodicalIF":0.0,"publicationDate":"2021-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45416862","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}
引用次数: 3
Left Annihilator of Identities with Generalized Derivations in Prime and Semiprime Rings 素数环和半素数环上广义导数恒等式的左湮灭子
Discussiones Mathematicae - General Algebra and Applications Pub Date : 2021-04-06 DOI: 10.7151/dmgaa.1356
Md. Hamidur Rahaman
{"title":"Left Annihilator of Identities with Generalized Derivations in Prime and Semiprime Rings","authors":"Md. Hamidur Rahaman","doi":"10.7151/dmgaa.1356","DOIUrl":"https://doi.org/10.7151/dmgaa.1356","url":null,"abstract":"Abstract Let R be a noncommutative prime ring of char (R) ≠ 2, F a generalized derivation of R associated to the derivation d of R and I a nonzero ideal of R. Let S ⊆ R. The left annihilator of S in R is denoted by lR(S) and defined by lR (S) = {x ∈ R | xS = 0}. In the present paper, we study the left annihilator of the sets {F (x)◦n F (y)−x◦n y | x, y ∈ I} and {F (x)◦n F (y)−d(x◦n y) | x, y ∈ I}.","PeriodicalId":36816,"journal":{"name":"Discussiones Mathematicae - General Algebra and Applications","volume":"41 1","pages":"69 - 79"},"PeriodicalIF":0.0,"publicationDate":"2021-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49159568","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}
引用次数: 0
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