In this paper we generalize Jacobsons results by proving that any integer  in   is a square-free integer), belong to . All units of  are generated by the fundamental unit  having the forms

our generalization build on using the conditions

This leads us to classify the real quadratic fields  into the sets  Jacobsons results shows that  and Sliwa confirm that  and  are the only real quadratic fields in .

This study came to discuss the subject of industries dependent on petrochemical industries in Iraq (plastic as a model) during the period 2005–2020, and the study concluded that the plastic industries contribute to areas of advancement and progress and opportunities to deal efficiently with the challenges posed by the new variables, the most important of which is the information revolution. communications and trade liberalization, and this is what contributes to the competitiveness of these industries. And because the petrochemical industry in Iraq has an active role in establishing plastic industrial clusters and clusters of micro, small, and medium industries by providing the necessary feedstock for these industries in various fields

Breast cancer constitutes about one fourth of the registered cancer cases among the Iraqi population (1)
and it is the leading cause of death among Iraqi women (2)
. Each year more women are exposed to the vicious
ramifications of this disease which include death if left unmanaged or the negative sequels that they would
experience, cosmetically and psychologically, after exposure to radical mastectomy.
The World Health Organization (WHO) documented that early detection and screening, when coped
with adequate therapy, could offer a reduction in breast cancer mortality; displaying that the low survival rates
in less developed countries, including Iraq, is mainly attributed to the lack of early detection programs couple

     The research aimed to identify the extent to which the media offices in the ministries depend on the website of the Iraqi Council of Ministers as a source of information. Such goal includes a set of sub-goals: Knowing the reasons for media offices' reliance on the information provided by the Cabinet's website; and revealing the benefit derived from relying on the Cabinet's website.

The researcher used the survey method to screen and comprehend the extent to which the media offices in the ministries depend on the website of the Iraqi Council of Ministers as a source of information.

The mechanism of comprehensive account of the limits of research wa

As human societies grow, the problem of waste management becomes one of the pressing issues that need to be addressed. Recycling and reuse of waste are effective waste management measures that prevent pollution and conserve natural resources. In this study, the possibility of using glass waste as an alternative was used as a partial weight substitute for fine aggregates with replacement ratios of 10, 20, 30, and 40% by the weight, and formed into test models (15 cm * 15 cm ) cube and (15 cm * 30 cm) cylinder, then matured and tested their strength compression and tensile strength at the age of 7 and 28 days and compared with a reference or conventional concrete with a mixing ratio (1: 1.5: 3) as well as testing its worka

Skin drug administration is the method used to provide drugs for local or systemic therapy, which is recognized for clinical usage. It is the third-largest method of medication delivery, after only intravenous administration and oral administration. Using a transdermal delivery method makes the administration easy, and blood concentration and adverse effects can be reduced. A microneedle is a micron-sized needle with a short height of no more than 500 micrometers and a width of no more than 50 micrometers. The needle comes into contact with the epidermal layer of the skin before it gets to the dermal layer, where there is no discomfort. Several materials, such as metals, inorganic, and polymer materials, are used to create microneed

The current study was conducted to demonstrate the effects of air pollution on different biochemical parameters inCitrus aurantium plant and calculation the Air Pollution Tolerance Index (APTI). Five sites were selected tocollect plant leaves, four of them within the city of Baghdad, namely Al-Jadriya, Al-Andlous, Al-Doura and closeto the private generators to represent the urban areas and Abu Ghraib site to represent the rural area. Seasonalsamples were collected for the period from October 2016 to June 2017. Eleven biochemical parameters totalchlorophyll, ascorbic acid, leaf extract pH, relative water content, total nitrogen, total protein content, total sugarcontent, proline, electrical conductivity, cadmium and lead. The results of Citr

Background: Osteoporosis is a skeletal defect manifested by a reduction of bone strength as a result of reduced bone mass to the extent that there is a higher risk of fracture even on minor trauma. Hysterectomy in a premenopausal woman is a well known cause of ovarian failure resulting in an increased risk of osteoporosis.

Objective : To clarify bisphosphonate's preventive effect on osteopenia and osteoporosis in premenopausal women after hysterectomy.

Type of the study: Cross –sectional study.

Method:  84 premenopausal females post hysterectomy aged between 40 – 50 years, were enrolled in this randomized controlled double blinded trail a

Abstract: As human history is implicated in landscape or the natural history, it can be stated that the origins of the Caribbean writers' conflict, in general, are the colonial history of West India. That history which tells the story behind not only their fragmented identity, but also the problems connected to their language as well. Building on the arguments of the prominent Postcolonial ecoccritics such as Elizabeth DeLoughrey, George Handley, Helen Tiffin, and Graham Huggan, this research analyzes selected poems by Derek Walcott's which are bounded in his volume, Collected Poems. It shows how the Caribbean history has been erased due to the brutality of colonization offering landscape as a reliable source which has recorded that history