in this paper we focus on a special class of commutative local rings called spap-rings and study the relationship between this class and other classes of rings. we characterize the structure of modules and especially, the prime submodules of free modules over an spap-ring and derive some basic properties. then we answer the question of lam and reyes about strongly oka ideals family. finally, we characterize the structure of spap-ring in special cases.
In this paper we focus on a special class of commutative local rings called SPAP-rings and study the relationship between this class and other classes of rings. We characterize the structure of modules and especially, the prime submodules of free modules over an SPAP-ring and der
Let $R$ be a commutative ring and $I$ an ideal of $R$. The zero-divisor graph of $R$ with respect to $I$, denoted by $Gamma_I(R)$, is the simple graph whose vertex set is ${x in Rsetminus I mid xy in I$, for some $y in Rsetminus I}$, with two distinct vertices $x$ and $y$ are adj
BACKGROUND Streptococcus mutans surface-protein antigen (SpaP, PAc, or antigen I/II) has been well known to play an important role in initial attachment to tooth surfaces. However, strains with weak SpaP-expression were recently reported to be found in natural populations of S. m
We present SPAP (Same Program for All Processors), a containerbased programming language for heterogeneous many-core systems. SPAP abstracts away processor-specific concurrency and performance concerns using containers. Each SPAP container is a high level primitive with an STL-li
AIM Streptococcus mutans and Streptococcus sobrinus are the main pathogens associated with the development of dental caries in humans. Recently, the real-time polymerase chain reaction (qPCR-TR) has been used for fast and exact quantification of these bacteria species. This molec
Background and Objective: Dental caries is the most common disease worldwide, and is a major healthcare problem. Streptococcus mutans is considered as the main factor causing dental caries. This study was conducted to assess Streptococcus mutans by its 16S rRNA gene and adhesin g