It is known that the filed product of two quasi-antiorders need not to be a quasi-antiorder. After some preparations, we give some sufficient conditions in order that the filed product of two quasi-antiorder relations on the same set is a quasi-antiorder again. 2000Mathematics Subject Classification: Primary 03F65, Secondary 04A05, 08A02

Lifting modules and their various generalizations as some main concepts in module theory have been studied and investigated extensively in recent decades. Some authors tried to present some homological aspects of lifting modules and -supplemented modules. In this work, we shall present a homological approach to -supplemented modules via fully invariant submodules. Lifting modules and H-suppleme...

is a module over the ring of all modular forms with respect to the group Γ2[4, 8]. We are interested in its structure. By Igusa, the ring of modular forms is generated by the ten classical theta constants θ[m]. The module M contains a submodule N which is generated by 45 Cohen-Rankin brackets {θ[m], θ[n]}. We determine defining relations for this submodule and compute its Hilbert function (Theo...

Mediator is a modular multiprotein complex required for regulated transcription by RNA polymerase (Pol) II. Here, we show that the middle module of the Mediator core contains a submodule of unique structure and function that comprises the N-terminal part of subunit Med7 (Med7N) and the highly conserved subunit Med31 (Soh1). The Med7N/31 submodule shows a conserved novel fold, with two proline-r...

Invertibility of multiplication modules All rings are commutative with 1 and all modules are unital. Let R be a ring and M an R-module. M is called multiplication if for each submodule N of M, N=IM for some ideal I of R. Multiplication modules have recently received considerable attention during the last twenty years. In this talk we give the de nition of invertible submodules as a natural gene...