Communications in Algebra

Nguyen, Bin

doi: 10.1080/00927872.2023.2232869pmid: N/A

Abstract Surfaces of general type with canonical map of degree d bigger than 8 have bounded geometric genus and irregularity. In particular the irregularity is at most 2 if d ≥ 10 . In the present paper, the existence of surfaces with d = 10 and all possible irregularities, surfaces with d = 12 and irregularity 1 and 2, and surfaces with d = 14 and irregularity 0 and 1 is proven, by constructing these surfaces as Z 2 3 -covers of certain rational surfaces. These results together with the construction by C. Rito of a surface with d = 12 and irregularity 0 show that all the possibilities for the irregularity in the cases d = 10, d = 12 can occur, whilst the existence of a surface with d = 14 and irregularity 2 is still an open problem.

Narisawa, Shota; Shirayanagi, Kiyoshi

doi: 10.1080/00927872.2023.2232875pmid: N/A

Abstract The crystal basis of an irreducible highest weight module of type A is realized by a combinatorial model called K-hives. In this paper, we give the tensor product decomposition map of crystal bases of irreducible highest weight modules of type A in terms of K-hives. In the process of constructing the decomposition map, we provide a combinatorial description on K-hives of the decomposition map.

Gupta, Pallavee; De Filippis, Vincenzo; Tiwari, S. K.

doi: 10.1080/00927872.2023.2233019pmid: N/A

Abstract Let R be a noncommutative prime ring of characteristic different from 2, Q r be the right Martindale quotient ring of R and C = Z ( Q r ) be the extended centroid of R . Suppose that π ( x 1 , … , x n ) is a noncentral multilinear polynomial over C , S = { π ( r 1 , … , r n ) | r 1 , … , r n ∈ R } , F , G and H are three generalized skew-derivations of R associated to the same automorphism α. Let h , f , g be the associated skew derivations respectively of H , F and G , such that h, f, g are commuting with α. We will provide the complete description of H , F and G , in the case F ( X ) G ( X ) = H ( X 2 ) , for all X ∈ S .

Asefa, Dadi

doi: 10.1080/00927872.2023.2233032pmid: N/A

Abstract– Let Δ ( 0 , 0 ) = ( A A N B B M A B ) be a Morita context ring with zero bimodule homomorphisms. We give sufficient conditions for modules over Δ ( 0 , 0 ) to be Ding projective.

Hyry, Eero; Klemetti, Markus

doi: 10.1080/00927872.2023.2234034pmid: N/A

Abstract Motivated by topological data analysis, we study in this article certain notions of “tameness” for modules over posets. In particular, we show that after adding infinitary points the so called finitely determined modules become finitely presented.

Öztürk, Mehmet Ali; Tekin, Özlem; Jun, Young Bae

doi: 10.1080/00927872.2023.2234037pmid: N/A

Abstract In 2022, Öztürk defined the nearness equivalence classes and nearness cosets of the nearness groups (see [10]). Furthermore, he showed a nearness group G induced by a nearness subgroup H can not be written two different decompositions of G by separate left (right) cosets [10]. In other words, if H is a nearness subgroup of a nearness group G, then G may be shown as a union of different non-discrete left (right) cosets of H in G. Also, it is given that Lagrange’s theorem does not work in the nearness subgroups as usual subgroups. Our purpose in this paper is to introduce normal nearness subgroups and quotient nearness groups. Besides which, it is given an example of a nearness group that has nearness subgroup but not normal nearness subgroup. Also, a criterion that satisfies the condition of being a normal subgroup is investigated. It is shown that the multiplication of the two right near-cosets (left near-cosets) is again a right near-coset (left near-coset) is valid in normal nearness subgroups under certain conditions. Moreover, examples of normal nearness subgroups and quotient nearness groups are given.

Zhang, Yafeng; Liu, Yu-Zhe; Ma, Yajun

doi: 10.1080/00927872.2023.2234999pmid: N/A

Abstract We give a sufficient condition that a certain homological epimorphism between two finite dimensional algebras induces a triangle equivalence between their Gorenstein defect categories as well as between their stable categories of Gorenstein projective modules.

Li, Haiyan; Liu, A.-Ming; Safonova, Inna N.; Skiba, Alexander N.

doi: 10.1080/00927872.2023.2235006pmid: N/A

Abstract Let X be a class of groups. Suppose that with each group G ∈ X we associate some system of its subgroups τ ( G ) . Then τ is said to be a subgroup functor (in the sense of Skiba) on X if the following conditions are hold: (1) G ∈ τ ( G ) for each group G ∈ X ; (2) for any epimorphism φ : A → B , where A , B ∈ X , and for any groups H ∈ τ ( A ) and T ∈ τ ( B ) we have H φ ∈ τ ( B ) and T φ − 1 ∈ τ ( A ) . In this paper, we discuss some applications of such subgroup functors in the theory of generalized T-groups.

Panasenko, Alexander Sergeevich

doi: 10.1080/00927872.2023.2235420pmid: N/A

Abstract We show that in a prime nonassociative Novikov algebra every nonzero ideal is non-associative. We prove that Baer (and Andrunakievich) radical and the largest left quasiregular ideal coincide in finite dimensional Novikov algebras over a field of characteristic 0 or algebraically closed field of odd characteristic. We show non-existence of right quasiregular radical in finite dimensional Novikov algebras.

Mao, Lixin

doi: 10.1080/00927872.2023.2235423pmid: N/A

Abstract Let R ⋉ M be a trivial extension of a ring R by an R-R-bimodule M. We first give some homological formulas over R ⋉ M . Then we investigate how to construct (hereditary, complete) cotorsion pairs and (hereditary, cofibrantly generated) Hovey triples over R ⋉ M . Finally, some applications are given in some Morita context rings.