Authors:Heinz Mitsch Pages: 361 - 380 Abstract: Algebra Colloquium, Volume 24, Issue 03, Page 361-380, September 2017. A semigroup (S, ·) is called right (left) quasiresiduated if for any a, b in S there exists x in S such that ax ≤S b (xa ≤S b) with respect to the natural partial order ≤S of S. This concept has its origin in the theory of residuated semigroups, but can also be seen as a generalization of the right (left) simplicity of semigroups. It is first studied for totally-, resp., trivially-ordered semigroups, and then for semigroups with idempotents. In particular, the cases when (S, ≤S) is directed downwards and when S contains a zero (with respect to a more restrictive definition) are dealt with. Throughout, examples are given; in total, 30 classes of (often well-known) semigroups of this kind are specified. Citation: Algebra Colloquium PubDate: 2017-09-15T08:52:24Z DOI: 10.1142/S1005386717000220

Authors:Rongquan Feng, Liwei Zeng, Yang Zhang Pages: 381 - 392 Abstract: Algebra Colloquium, Volume 24, Issue 03, Page 381-392, September 2017. In this paper, we construct some [math]-designs, which are also known as partial geometric designs, using totally isotropic subspaces of the unitary space. Furthermore, these [math]-designs yield six infinite families of directed strongly regular graphs. Citation: Algebra Colloquium PubDate: 2017-09-15T08:52:21Z DOI: 10.1142/S1005386717000232

Authors:Nadeem Ahmad Dar, Abdul Nadim Khan Pages: 393 - 399 Abstract: Algebra Colloquium, Volume 24, Issue 03, Page 393-399, September 2017. The main purpose of this paper is to study generalized derivations in rings with involution which behave like strong commutativity preserving mappings. In fact, we prove the following result: Let R be a noncommutative prime ring with involution of the second kind such that char [math]. If R admits a generalized derivation [math] associated with a derivation [math] such that [math] for all [math], then [math] for all [math] or [math] for all [math]. Moreover, a related result is also obtained. Citation: Algebra Colloquium PubDate: 2017-09-15T08:52:24Z DOI: 10.1142/S1005386717000244

Authors:Hassan Haghighi, Siamak Yassemi, Rahim Zaare-Nahandi Pages: 401 - 406 Abstract: Algebra Colloquium, Volume 24, Issue 03, Page 401-406, September 2017. We characterize pure lexsegment complexes which are Cohen-Macaulay in arbitrary codimension. More precisely, we prove that any lexsegment complex is Cohen-Macaulay if and only if it is pure and its 1-dimensional links are connected, and that a lexsegment flag complex is Cohen-Macaulay if and only if it is pure and connected. We show that any non-Cohen-Macaulay lexsegment complex is a Buchsbaum complex if and only if it is a pure disconnected flag complex. For [math], a lexsegment complex is strictly Cohen-Macaulay in codimension t if and only if it is the join of a lexsegment pure disconnected flag complex with a [math]-dimensional simplex. When the Stanley-Reisner ideal of a pure lexsegment complex is not quadratic, the complex is Cohen-Macaulay if and only if it is Cohen-Macaulay in some codimension. Our results are based on a characterization of Cohen-Macaulay and Buchsbaum lexsegment complexes by Bonanzinga, Sorrenti and Terai. Citation: Algebra Colloquium PubDate: 2017-09-15T08:52:22Z DOI: 10.1142/S1005386717000256

Authors:Xin Tang Pages: 419 - 438 Abstract: Algebra Colloquium, Volume 24, Issue 03, Page 419-438, September 2017. We study a family of “symmetric” multiparameter quantized Weyl algebras [math] and some related algebras. We compute the Nakayama automorphism of [math], give a necessary and sufficient condition for [math] to be Calabi-Yau, and prove that [math] is cancellative. We study the automorphisms and isomorphism problem for [math] and [math]. Similar results are established for the Maltsiniotis multiparameter quantized Weyl algebra [math] and its polynomial extension. We prove a quantum analogue of the Dixmier conjecture for a simple localization [math] and determine its automorphism group. Citation: Algebra Colloquium PubDate: 2017-09-15T08:52:30Z DOI: 10.1142/S100538671700027X

Authors:Shigeo Koshitani, Jürgen Müller Pages: 439 - 452 Abstract: Algebra Colloquium, Volume 24, Issue 03, Page 439-452, September 2017. We give a lower bound of the Loewy length of the projective cover of the trivial module for the group algebra kG of a finite group G of Lie type defined over a finite field of odd characteristic p, where k is an arbitrary field of characteristic p. The proof uses Auslander-Reiten theory. Citation: Algebra Colloquium PubDate: 2017-09-15T08:52:23Z DOI: 10.1142/S1005386717000281

Authors:Songtao Guo, Hailong Hou, Yong Xu Pages: 453 - 466 Abstract: Algebra Colloquium, Volume 24, Issue 03, Page 453-466, September 2017. A graph is symmetric if its automorphism group acts transitively on the set of arcs of the graph. We classify connected heptavalent symmetric graphs of order 16p for each prime p. As a result, there are two such sporadic graphs with p = 3 and 7, and an infinite family of 1-regular normal Cayley graphs on the group [math] with 7 (p – 1). Citation: Algebra Colloquium PubDate: 2017-09-15T08:52:31Z DOI: 10.1142/S1005386717000293

Authors:M.R. Darafsheh, M. Abdollahi Pages: 467 - 480 Abstract: Algebra Colloquium, Volume 24, Issue 03, Page 467-480, September 2017. In this paper we determine all tetravalent Cayley graphs of a non-abelian group of order 3p2, where p is a prime number greater than 3, and with a cyclic Sylow p-subgroup. We show that all of these tetravalent Cayley graphs are normal. The full automorphism group of these Cayley graphs is given and the half-transitivity and the arc-transitivity of these graphs are investigated. We show that this group is a 5-CI-group. Citation: Algebra Colloquium PubDate: 2017-09-15T08:52:20Z DOI: 10.1142/S100538671700030X

Authors:Dhiren Kumar Basnet, Jayanta Bhattacharyya Pages: 481 - 492 Abstract: Algebra Colloquium, Volume 24, Issue 03, Page 481-492, September 2017. In this article, we define the nil clean graph of a ring R. The vertex set is the ring R, and two ring elements a and b are adjacent if and only if a + b is nil clean in R. Graph theoretic properties like the girth, dominating sets, diameter, etc., of the nil clean graph are studied for finite commutative rings. Citation: Algebra Colloquium PubDate: 2017-09-15T08:52:23Z DOI: 10.1142/S1005386717000311

Authors:Samaneh Tabejamaat, Amir Mafi, Khadijeh Ahmadi Amoli Pages: 509 - 518 Abstract: Algebra Colloquium, Volume 24, Issue 03, Page 509-518, September 2017. Let (R, m) be a Cohen–Macaulay local ring of dimension d, C a canonical R-module and M an almost Cohen–Macaulay R-module of dimension n and of depth t. We prove that dim [math] and if [math] then [math] is an almost Cohen–Macaulay R-module. In particular, if [math] then HomR(M, C) is an almost Cohen–Macaulay R-module. In addition, with some conditions, we show that [math] is also almost Cohen–Macaulay. Finally, we study the vanishing [math] and [math]. Citation: Algebra Colloquium PubDate: 2017-09-15T08:52:21Z DOI: 10.1142/S1005386717000335

Authors:Ruipu Bai, Lixin Lin, Yan Zhang, Chuangchuang Kang Pages: 519 - 540 Abstract: Algebra Colloquium, Volume 24, Issue 03, Page 519-540, September 2017. q-Deformations of 3-Lie algebras and representations of q-3-Lie algebras are discussed. A q-3-Lie algebra [math], where [math] and [math], is a vector space A over a field ð”½ with 3-ary linear multiplications [ , , ]q and [math] from [math] to A, and a map [math] satisfying the q-Jacobi identity [math] for all [math]. If the multiplications satisfy that [math] and [math] is skew-symmetry, then [math] is called a type (I)-q-3- Lie algebra. From q-Lie algebras, group algebras and commutative associative algebras, q-3-Lie algebras and type (I)-q-3-Lie algebras are constructed. Also, the non-trivial onedimensional central extension of q-3-Lie algebras is investigated, and new q-3-Lie algebras [math], and [math] are obtained. Citation: Algebra Colloquium PubDate: 2017-09-15T08:52:26Z DOI: 10.1142/S1005386717000347